<!DOCTYPE html><html lang="zh-CN"><head><meta charset="utf-8"><meta name="X-UA-Compatible" content="IE=edge"><meta name="author" content="imp"><title>LaTex数学公式符号 · imp的个人博客</title><meta name="description" content="基本符号
小写希腊字母
注：部分希腊字母在数学公式中常以变量形式出现，例如ϵ\epsilonϵ在数学中一般写法为ε\varepsilonε



符号
语法
符号
语法
符号
语法




α\alphaα
\alpha
β\betaβ
\beta
γ\gammaγ
\gamm


θ\thetaθ"><meta name="keywords" content="imp,blog"><meta content="width=device-width, initial-scale=1.0, maximum-scale=1.0, user-scalable=0" name="viewport"><meta content="yes" name="apple-mobile-web-app-capable"><meta content="black" name="apple-mobile-web-app-status-bar-style"><meta content="telephone=no" name="format-detection"><meta id="site_root_url" data="/"><meta id="default-theme" data="light"><meta name="renderer" content="webkit"><link rel="shortcut icon" type="image/x-icon" href="/images/icon.png"><link rel="stylesheet" href="/css/theme/light.css"><link rel="stylesheet" href="/css/style.css"><link rel="stylesheet" href="/css/blog_basic.css"><link rel="stylesheet" href="/css/font-awesome.min.css"><link rel="stylesheet" href="/css/insight.css"><link rel="stylesheet" href="/css/search.css"><link rel="alternate" type="application/atom+xml" title="ATOM 1.0" href="/atom.xml"><script src="/js/url_for.js"></script><script src="/js/friends-link-generator.js"></script><script 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in-page animated fadeInDown"><div class="toclist-container"><div class="tocmenu"><ol class="toclist"><li class="toclist-item toclist-level-2"><a class="toclist-link" href="#%E5%9F%BA%E6%9C%AC%E7%AC%A6%E5%8F%B7"><span class="toclist-text">基本符号</span></a><ol class="toclist-child"><li class="toclist-item toclist-level-3"><a class="toclist-link" href="#%E5%B0%8F%E5%86%99%E5%B8%8C%E8%85%8A%E5%AD%97%E6%AF%8D"><span class="toclist-text">小写希腊字母</span></a></li><li class="toclist-item toclist-level-3"><a class="toclist-link" href="#%E5%A4%A7%E5%86%99%E5%B8%8C%E8%85%8A%E5%AD%97%E6%AF%8D"><span class="toclist-text">大写希腊字母</span></a></li><li class="toclist-item toclist-level-3"><a class="toclist-link" href="#%E5%B8%B8%E7%94%A8%E5%AD%97%E4%BD%93"><span class="toclist-text">常用字体</span></a></li><li class="toclist-item toclist-level-3"><a class="toclist-link" href="#%E5%B8%B8%E8%A7%81%E8%BF%90%E7%AE%97%E7%AC%A6"><span class="toclist-text">常见运算符</span></a></li><li class="toclist-item toclist-level-3"><a class="toclist-link" href="#%E5%A4%A7%E5%B0%BA%E5%AF%B8%E8%BF%90%E7%AE%97%E7%AC%A6"><span class="toclist-text">大尺寸运算符</span></a></li><li class="toclist-item toclist-level-3"><a class="toclist-link" href="#%E5%B8%B8%E8%A7%81%E5%85%B3%E7%B3%BB%E7%AC%A6%E5%8F%B7"><span class="toclist-text">常见关系符号</span></a></li><li class="toclist-item toclist-level-3"><a class="toclist-link" href="#%E6%95%B0%E5%AD%A6%E6%A8%A1%E5%BC%8F%E9%87%8D%E9%9F%B3%E7%AC%A6"><span class="toclist-text">数学模式重音符</span></a></li><li class="toclist-item toclist-level-3"><a class="toclist-link" href="#%E7%AE%AD%E5%A4%B4"><span class="toclist-text">箭头</span></a></li><li class="toclist-item toclist-level-3"><a class="toclist-link" href="#%E6%8B%AC%E5%8F%B7"><span class="toclist-text">括号</span></a></li><li class="toclist-item toclist-level-3"><a class="toclist-link" href="#%E5%A4%A7%E5%B0%BA%E5%AF%B8%E6%8B%AC%E5%8F%B7"><span class="toclist-text">大尺寸括号</span></a></li><li class="toclist-item toclist-level-3"><a class="toclist-link" href="#%E5%85%B6%E4%BB%96%E5%B8%B8%E8%A7%81%E7%AC%A6%E5%8F%B7"><span class="toclist-text">其他常见符号</span></a></li></ol></li><li class="toclist-item toclist-level-2"><a class="toclist-link" href="#%E6%95%B0%E5%AD%A6%E5%85%AC%E5%BC%8F%E5%86%99%E6%B3%95"><span class="toclist-text">数学公式写法</span></a><ol class="toclist-child"><li class="toclist-item toclist-level-3"><a class="toclist-link" href="#%E4%B8%8A%E4%B8%8B%E6%A0%87"><span class="toclist-text">上下标</span></a></li><li class="toclist-item toclist-level-3"><a class="toclist-link" href="#%E5%88%86%E6%95%B0"><span class="toclist-text">分数</span></a></li><li class="toclist-item toclist-level-3"><a class="toclist-link" href="#%E6%8F%92%E5%85%A5%E6%96%87%E5%AD%97"><span class="toclist-text">插入文字</span></a></li><li class="toclist-item toclist-level-3"><a class="toclist-link" href="#%E5%B8%B8%E8%A7%81%E5%87%BD%E6%95%B0"><span class="toclist-text">常见函数</span></a></li><li class="toclist-item toclist-level-3"><a class="toclist-link" href="#%E7%9F%A9%E9%98%B5%E3%80%81%E8%A1%8C%E5%88%97%E5%BC%8F"><span class="toclist-text">矩阵、行列式</span></a></li><li class="toclist-item toclist-level-3"><a class="toclist-link" href="#%E5%A4%9A%E8%A1%8C%E5%85%AC%E5%BC%8F%E5%AF%B9%E9%BD%90"><span class="toclist-text">多行公式对齐</span></a></li><li class="toclist-item toclist-level-3"><a class="toclist-link" href="#%E6%96%B9%E7%A8%8B%E7%BB%84"><span class="toclist-text">方程组</span></a></li></ol></li></ol></div></div></div></div><div class="sidebar animated"><div class="sidebar-top"><div class="logo-title"><div class="title"><img src="/images/avatar.png" style="width:220px;" alt="favicon"><h3 title=""><a href="/">imp的个人博客</a></h3><div class="description"><p>A simple blog</p></div></div><ul class="social-links"><li><a target="_blank" rel="noopener" href="https://github.com/Dimp07"><i class="fa fa-github"></i></a></li><li><a href="mailto:610634344@qq.com"><i class="fa fa-envelope"></i></a></li></ul></div><div class="toc-container in-sidebar animated fadeInDown"><details class="ltr" open><summary>目录</summary><div class="toclist-container"><div class="tocmenu"><ol class="toclist"><li class="toclist-item toclist-level-2"><a class="toclist-link" href="#%E5%9F%BA%E6%9C%AC%E7%AC%A6%E5%8F%B7"><span class="toclist-text">基本符号</span></a><ol class="toclist-child"><li class="toclist-item toclist-level-3"><a class="toclist-link" href="#%E5%B0%8F%E5%86%99%E5%B8%8C%E8%85%8A%E5%AD%97%E6%AF%8D"><span class="toclist-text">小写希腊字母</span></a></li><li class="toclist-item toclist-level-3"><a class="toclist-link" href="#%E5%A4%A7%E5%86%99%E5%B8%8C%E8%85%8A%E5%AD%97%E6%AF%8D"><span class="toclist-text">大写希腊字母</span></a></li><li class="toclist-item toclist-level-3"><a class="toclist-link" href="#%E5%B8%B8%E7%94%A8%E5%AD%97%E4%BD%93"><span class="toclist-text">常用字体</span></a></li><li class="toclist-item toclist-level-3"><a class="toclist-link" href="#%E5%B8%B8%E8%A7%81%E8%BF%90%E7%AE%97%E7%AC%A6"><span class="toclist-text">常见运算符</span></a></li><li class="toclist-item toclist-level-3"><a class="toclist-link" href="#%E5%A4%A7%E5%B0%BA%E5%AF%B8%E8%BF%90%E7%AE%97%E7%AC%A6"><span class="toclist-text">大尺寸运算符</span></a></li><li class="toclist-item toclist-level-3"><a class="toclist-link" href="#%E5%B8%B8%E8%A7%81%E5%85%B3%E7%B3%BB%E7%AC%A6%E5%8F%B7"><span class="toclist-text">常见关系符号</span></a></li><li class="toclist-item toclist-level-3"><a class="toclist-link" href="#%E6%95%B0%E5%AD%A6%E6%A8%A1%E5%BC%8F%E9%87%8D%E9%9F%B3%E7%AC%A6"><span class="toclist-text">数学模式重音符</span></a></li><li class="toclist-item toclist-level-3"><a class="toclist-link" href="#%E7%AE%AD%E5%A4%B4"><span class="toclist-text">箭头</span></a></li><li class="toclist-item toclist-level-3"><a class="toclist-link" href="#%E6%8B%AC%E5%8F%B7"><span class="toclist-text">括号</span></a></li><li class="toclist-item toclist-level-3"><a class="toclist-link" href="#%E5%A4%A7%E5%B0%BA%E5%AF%B8%E6%8B%AC%E5%8F%B7"><span class="toclist-text">大尺寸括号</span></a></li><li class="toclist-item toclist-level-3"><a class="toclist-link" href="#%E5%85%B6%E4%BB%96%E5%B8%B8%E8%A7%81%E7%AC%A6%E5%8F%B7"><span class="toclist-text">其他常见符号</span></a></li></ol></li><li class="toclist-item toclist-level-2"><a class="toclist-link" href="#%E6%95%B0%E5%AD%A6%E5%85%AC%E5%BC%8F%E5%86%99%E6%B3%95"><span class="toclist-text">数学公式写法</span></a><ol class="toclist-child"><li class="toclist-item toclist-level-3"><a class="toclist-link" href="#%E4%B8%8A%E4%B8%8B%E6%A0%87"><span class="toclist-text">上下标</span></a></li><li class="toclist-item toclist-level-3"><a class="toclist-link" href="#%E5%88%86%E6%95%B0"><span class="toclist-text">分数</span></a></li><li class="toclist-item toclist-level-3"><a class="toclist-link" href="#%E6%8F%92%E5%85%A5%E6%96%87%E5%AD%97"><span class="toclist-text">插入文字</span></a></li><li class="toclist-item toclist-level-3"><a class="toclist-link" href="#%E5%B8%B8%E8%A7%81%E5%87%BD%E6%95%B0"><span class="toclist-text">常见函数</span></a></li><li class="toclist-item toclist-level-3"><a class="toclist-link" href="#%E7%9F%A9%E9%98%B5%E3%80%81%E8%A1%8C%E5%88%97%E5%BC%8F"><span class="toclist-text">矩阵、行列式</span></a></li><li class="toclist-item toclist-level-3"><a class="toclist-link" href="#%E5%A4%9A%E8%A1%8C%E5%85%AC%E5%BC%8F%E5%AF%B9%E9%BD%90"><span class="toclist-text">多行公式对齐</span></a></li><li class="toclist-item toclist-level-3"><a class="toclist-link" href="#%E6%96%B9%E7%A8%8B%E7%BB%84"><span class="toclist-text">方程组</span></a></li></ol></li></ol></div></div></details></div></div><div class="footer"><div class="p"> <span>  </span><i class="fa fa-star"></i><span> imp</span></div><div class="by_farbox"><span>Powered by </span><a href="https://hexo.io/zh-cn/" target="_blank">Hexo </a><span> & </span><a href="https://github.com/Lhcfl/hexo-theme-anatolo" target="_blank">Anatolo </a></div><div class="beian"></div></div></div><div class="main animated fadeInDown"><div class="autopagerize_page_element"><div class="content"><div class="post-page"><div class="post animated"><div class="post-title"><h3><a>LaTex数学公式符号</a></h3></div><div class="post-content"><p><h2 id="基本符号">基本符号</h2>
<h3 id="小写希腊字母">小写希腊字母</h3>
<p><strong>注：部分希腊字母在数学公式中常以变量形式出现，例如<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>ϵ</mi></mrow><annotation encoding="application/x-tex">\epsilon</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal">ϵ</span></span></span></span>在数学中一般写法为<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>ε</mi></mrow><annotation encoding="application/x-tex">\varepsilon</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal">ε</span></span></span></span></strong></p>
<table>
<thead>
<tr>
<th style="text-align:center">符号</th>
<th style="text-align:center">语法</th>
<th style="text-align:center">符号</th>
<th style="text-align:center">语法</th>
<th style="text-align:center">符号</th>
<th style="text-align:center">语法</th>
</tr>
</thead>
<tbody>
<tr>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>α</mi></mrow><annotation encoding="application/x-tex">\alpha</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal" style="margin-right:0.0037em;">α</span></span></span></span></td>
<td style="text-align:center">\alpha</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>β</mi></mrow><annotation encoding="application/x-tex">\beta</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.05278em;">β</span></span></span></span></td>
<td style="text-align:center">\beta</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>γ</mi></mrow><annotation encoding="application/x-tex">\gamma</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.05556em;">γ</span></span></span></span></td>
<td style="text-align:center">\gamm</td>
</tr>
<tr>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>θ</mi></mrow><annotation encoding="application/x-tex">\theta</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">θ</span></span></span></span></td>
<td style="text-align:center">\theta</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>ε</mi></mrow><annotation encoding="application/x-tex">\varepsilon</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal">ε</span></span></span></span></td>
<td style="text-align:center">\varepsilo</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>δ</mi></mrow><annotation encoding="application/x-tex">\delta</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord mathnormal" style="margin-right:0.03785em;">δ</span></span></span></span></td>
<td style="text-align:center">\delta</td>
</tr>
<tr>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>μ</mi></mrow><annotation encoding="application/x-tex">\mu</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">μ</span></span></span></span></td>
<td style="text-align:center">\mu</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>ν</mi></mrow><annotation encoding="application/x-tex">\nu</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal" style="margin-right:0.06366em;">ν</span></span></span></span></td>
<td style="text-align:center">\nu</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>η</mi></mrow><annotation encoding="application/x-tex">\eta</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">η</span></span></span></span></td>
<td style="text-align:center">\eta</td>
</tr>
<tr>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>ζ</mi></mrow><annotation encoding="application/x-tex">\zeta</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.07378em;">ζ</span></span></span></span></td>
<td style="text-align:center">\zeta</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>λ</mi></mrow><annotation encoding="application/x-tex">\lambda</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord mathnormal">λ</span></span></span></span></td>
<td style="text-align:center">\lambda</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>ψ</mi></mrow><annotation encoding="application/x-tex">\psi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">ψ</span></span></span></span></td>
<td style="text-align:center">\psi</td>
</tr>
<tr>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>σ</mi></mrow><annotation encoding="application/x-tex">\sigma</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">σ</span></span></span></span></td>
<td style="text-align:center">\sigma</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>ξ</mi></mrow><annotation encoding="application/x-tex">\xi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.04601em;">ξ</span></span></span></span></td>
<td style="text-align:center">\xi</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>τ</mi></mrow><annotation encoding="application/x-tex">\tau</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal" style="margin-right:0.1132em;">τ</span></span></span></span></td>
<td style="text-align:center">\tau</td>
</tr>
<tr>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>ϕ</mi></mrow><annotation encoding="application/x-tex">\phi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">ϕ</span></span></span></span></td>
<td style="text-align:center">\phi</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>φ</mi></mrow><annotation encoding="application/x-tex">\varphi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">φ</span></span></span></span></td>
<td style="text-align:center">\varphi</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>ρ</mi></mrow><annotation encoding="application/x-tex">\rho</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">ρ</span></span></span></span></td>
<td style="text-align:center">\rho</td>
</tr>
<tr>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>χ</mi></mrow><annotation encoding="application/x-tex">\chi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">χ</span></span></span></span></td>
<td style="text-align:center">\chi</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>ω</mi></mrow><annotation encoding="application/x-tex">\omega</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">ω</span></span></span></span></td>
<td style="text-align:center">\omega</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>π</mi></mrow><annotation encoding="application/x-tex">\pi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">π</span></span></span></span></td>
<td style="text-align:center">\pi</td>
</tr>
</tbody>
</table>
<h3 id="大写希腊字母">大写希腊字母</h3>
<p>大写希腊字母通常是小写希腊字母的LATEX语法第一个字母改为大写，见下表</p>
<table>
<thead>
<tr>
<th style="text-align:center">符号</th>
<th style="text-align:center">语法</th>
<th style="text-align:center">符号</th>
<th style="text-align:center">语法</th>
<th style="text-align:center">符号</th>
<th style="text-align:center">语法</th>
</tr>
</thead>
<tbody>
<tr>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>S</mi><mi>i</mi><mi>g</mi><mi>m</mi><mi>a</mi></mrow><annotation encoding="application/x-tex">Sigma</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8778em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.05764em;">S</span><span class="mord mathnormal">i</span><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="mord mathnormal">ma</span></span></span></span></td>
<td style="text-align:center">\Sigma</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mi>i</mi></mrow><annotation encoding="application/x-tex">Pi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mord mathnormal">i</span></span></span></span></td>
<td style="text-align:center">\Pi</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>D</mi><mi>e</mi><mi>l</mi><mi>t</mi><mi>a</mi></mrow><annotation encoding="application/x-tex">Delta</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord mathnormal">De</span><span class="mord mathnormal">lt</span><span class="mord mathnormal">a</span></span></span></span></td>
<td style="text-align:center">\Delta</td>
</tr>
<tr>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>G</mi><mi>a</mi><mi>m</mi><mi>m</mi><mi>a</mi></mrow><annotation encoding="application/x-tex">Gamma</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal">G</span><span class="mord mathnormal">amma</span></span></span></span></td>
<td style="text-align:center">\Gamma</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mi>s</mi><mi>i</mi></mrow><annotation encoding="application/x-tex">Psi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mord mathnormal">s</span><span class="mord mathnormal">i</span></span></span></span></td>
<td style="text-align:center">\Psi</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>T</mi><mi>h</mi><mi>e</mi><mi>t</mi><mi>a</mi></mrow><annotation encoding="application/x-tex">Theta</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">T</span><span class="mord mathnormal">h</span><span class="mord mathnormal">e</span><span class="mord mathnormal">t</span><span class="mord mathnormal">a</span></span></span></span></td>
<td style="text-align:center">\Theta</td>
</tr>
<tr>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>L</mi><mi>a</mi><mi>m</mi><mi>b</mi><mi>d</mi><mi>a</mi></mrow><annotation encoding="application/x-tex">Lambda</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord mathnormal">L</span><span class="mord mathnormal">amb</span><span class="mord mathnormal">d</span><span class="mord mathnormal">a</span></span></span></span></td>
<td style="text-align:center">\Lambda</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>O</mi><mi>m</mi><mi>e</mi><mi>g</mi><mi>a</mi></mrow><annotation encoding="application/x-tex">Omega</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8778em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">O</span><span class="mord mathnormal">m</span><span class="mord mathnormal">e</span><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="mord mathnormal">a</span></span></span></span></td>
<td style="text-align:center">\Omega</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mi>h</mi><mi>i</mi></mrow><annotation encoding="application/x-tex">Phi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mord mathnormal">hi</span></span></span></span></td>
<td style="text-align:center">\Phi</td>
</tr>
<tr>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>X</mi><mi>i</mi></mrow><annotation encoding="application/x-tex">Xi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.07847em;">X</span><span class="mord mathnormal">i</span></span></span></span></td>
<td style="text-align:center">\Xi</td>
<td style="text-align:center"></td>
<td style="text-align:center"></td>
<td style="text-align:center"></td>
<td style="text-align:center"></td>
</tr>
</tbody>
</table>
<h3 id="常用字体">常用字体</h3>
<p>默认的字体为<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>A</mi><mi>B</mi><mi>C</mi><mi>d</mi><mi>e</mi><mi>f</mi></mrow><annotation encoding="application/x-tex">ABCdef</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">A</span><span class="mord mathnormal" style="margin-right:0.07153em;">BC</span><span class="mord mathnormal">d</span><span class="mord mathnormal">e</span><span class="mord mathnormal" style="margin-right:0.10764em;">f</span></span></span></span>，也就是\mathnormal{ABCdef}（当然，打公式的时候不需要加上这个\mathnormal，直接打字母就是这个效果）</p>
<table>
<thead>
<tr>
<th style="text-align:center">字体</th>
<th style="text-align:center">语法</th>
<th style="text-align:center">字体</th>
<th style="text-align:center">语法</th>
</tr>
</thead>
<tbody>
<tr>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>m</mi><mi>a</mi><mi>t</mi><mi>h</mi><mi>r</mi><mi>m</mi><mrow><mi>A</mi><mi>B</mi><mi>C</mi><mi>d</mi><mi>e</mi><mi>f</mi></mrow><mi>A</mi><mi>B</mi><mi>C</mi><mi>d</mi><mi>e</mi></mrow><annotation encoding="application/x-tex">mathrm{ABCdef}ABCde</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">ma</span><span class="mord mathnormal">t</span><span class="mord mathnormal">h</span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mord mathnormal">m</span><span class="mord"><span class="mord mathnormal">A</span><span class="mord mathnormal" style="margin-right:0.07153em;">BC</span><span class="mord mathnormal">d</span><span class="mord mathnormal">e</span><span class="mord mathnormal" style="margin-right:0.10764em;">f</span></span><span class="mord mathnormal">A</span><span class="mord mathnormal" style="margin-right:0.07153em;">BC</span><span class="mord mathnormal">d</span><span class="mord mathnormal">e</span></span></span></span></td>
<td style="text-align:center">\mathrm{ABCdef}ABCde</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><mi mathvariant="bold">A</mi><mi mathvariant="bold">B</mi><mi mathvariant="bold">C</mi><mi mathvariant="bold">d</mi><mi mathvariant="bold">e</mi><mi mathvariant="bold">f</mi></mrow><mi>A</mi><mi>B</mi><mi>C</mi><mi>d</mi><mi>e</mi></mrow><annotation encoding="application/x-tex">\mathbf{ABCdef}ABCde</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord"><span class="mord mathbf" style="margin-right:0.10903em;">ABCdef</span></span><span class="mord mathnormal">A</span><span class="mord mathnormal" style="margin-right:0.07153em;">BC</span><span class="mord mathnormal">d</span><span class="mord mathnormal">e</span></span></span></span></td>
<td style="text-align:center">\mathbf{ABCdef}ABCde</td>
</tr>
<tr>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><mi>A</mi><mi>B</mi><mi>C</mi><mi>d</mi><mi>e</mi><mi>f</mi></mrow><mi>A</mi><mi>B</mi><mi>C</mi><mi>d</mi><mi>e</mi></mrow><annotation encoding="application/x-tex">\mathit{ABCdef}ABCde</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord"><span class="mord mathit">ABCdef</span></span><span class="mord mathnormal">A</span><span class="mord mathnormal" style="margin-right:0.07153em;">BC</span><span class="mord mathnormal">d</span><span class="mord mathnormal">e</span></span></span></span></td>
<td style="text-align:center">\mathit{ABCdef}ABCde</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mstyle style="text-shadow: 0.02em 0.01em 0.04px"><mi>A</mi><mi>B</mi><mi>C</mi><mi>d</mi><mi>e</mi><mi>f</mi></mstyle><mi>A</mi><mi>B</mi><mi>C</mi><mi>d</mi><mi>e</mi></mrow><annotation encoding="application/x-tex">\pmb{ABCdef}ABCde</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord" style="text-shadow:0.02em 0.01em 0.04px;"><span class="mord mathnormal">A</span><span class="mord mathnormal" style="margin-right:0.07153em;">BC</span><span class="mord mathnormal">d</span><span class="mord mathnormal">e</span><span class="mord mathnormal" style="margin-right:0.10764em;">f</span></span><span class="mord mathnormal">A</span><span class="mord mathnormal" style="margin-right:0.07153em;">BC</span><span class="mord mathnormal">d</span><span class="mord mathnormal">e</span></span></span></span></td>
<td style="text-align:center">\pmb{ABCdef}ABCde</td>
</tr>
<tr>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><mi mathvariant="script">A</mi><mi mathvariant="script">B</mi><mi mathvariant="script">C</mi><mi mathvariant="script">d</mi><mi mathvariant="script">e</mi><mi mathvariant="script">f</mi></mrow><mi>A</mi><mi>B</mi><mi>C</mi><mi>d</mi><mi>e</mi></mrow><annotation encoding="application/x-tex">\mathscr{ABCdef}ABCde</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8944em;vertical-align:-0.1944em;"></span><span class="mord"><span class="mord mathscr" style="margin-right:0.1689em;">ABC</span><span class="mord mathnormal">d</span><span class="mord mathnormal">e</span><span class="mord mathnormal" style="margin-right:0.10764em;">f</span></span><span class="mord mathnormal">A</span><span class="mord mathnormal" style="margin-right:0.07153em;">BC</span><span class="mord mathnormal">d</span><span class="mord mathnormal">e</span></span></span></span></td>
<td style="text-align:center">\mathscr{ABCdef}ABCde</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><mi mathvariant="script">A</mi><mi mathvariant="script">B</mi><mi mathvariant="script">C</mi><mi mathvariant="script">d</mi><mi mathvariant="script">e</mi><mi mathvariant="script">f</mi></mrow><mi>A</mi><mi>B</mi><mi>C</mi><mi>d</mi><mi>e</mi></mrow><annotation encoding="application/x-tex">\mathcal{ABCdef}ABCde</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord"><span class="mord mathcal">A</span><span class="mord mathcal" style="margin-right:0.05834em;">BC</span><span class="mord mathnormal">d</span><span class="mord mathnormal">e</span><span class="mord mathnormal" style="margin-right:0.10764em;">f</span></span><span class="mord mathnormal">A</span><span class="mord mathnormal" style="margin-right:0.07153em;">BC</span><span class="mord mathnormal">d</span><span class="mord mathnormal">e</span></span></span></span></td>
<td style="text-align:center">\mathcal{ABCdef}ABCde</td>
</tr>
<tr>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><mi mathvariant="fraktur">A</mi><mi mathvariant="fraktur">B</mi><mi mathvariant="fraktur">C</mi><mi mathvariant="fraktur">d</mi><mi mathvariant="fraktur">e</mi><mi mathvariant="fraktur">f</mi></mrow><mi>A</mi><mi>B</mi><mi>C</mi><mi>d</mi><mi>e</mi></mrow><annotation encoding="application/x-tex">\mathfrak{ABCdef}ABCde</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8835em;vertical-align:-0.1891em;"></span><span class="mord"><span class="mord mathfrak">ABCdef</span></span><span class="mord mathnormal">A</span><span class="mord mathnormal" style="margin-right:0.07153em;">BC</span><span class="mord mathnormal">d</span><span class="mord mathnormal">e</span></span></span></span></td>
<td style="text-align:center">\mathfrak{ABCdef}ABCde</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><mi mathvariant="double-struck">A</mi><mi mathvariant="double-struck">B</mi><mi mathvariant="double-struck">C</mi><mi mathvariant="double-struck">d</mi><mi mathvariant="double-struck">e</mi><mi mathvariant="double-struck">f</mi></mrow><mi>A</mi><mi>B</mi><mi>C</mi><mi>d</mi><mi>e</mi></mrow><annotation encoding="application/x-tex">\mathbb{ABCdef}ABCde</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord"><span class="mord mathbb">ABC</span><span class="mord mathnormal">d</span><span class="mord mathnormal">e</span><span class="mord mathnormal" style="margin-right:0.10764em;">f</span></span><span class="mord mathnormal">A</span><span class="mord mathnormal" style="margin-right:0.07153em;">BC</span><span class="mord mathnormal">d</span><span class="mord mathnormal">e</span></span></span></span></td>
<td style="text-align:center">\mathbb{ABCdef}ABCde</td>
</tr>
</tbody>
</table>
<h3 id="常见运算符">常见运算符</h3>
<table>
<thead>
<tr>
<th style="text-align:center">运算符</th>
<th style="text-align:center">语法</th>
<th style="text-align:center">运算符</th>
<th style="text-align:center">语法</th>
<th style="text-align:center">运算符</th>
<th style="text-align:center">语法</th>
</tr>
</thead>
<tbody>
<tr>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>+</mo></mrow><annotation encoding="application/x-tex">+</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">+</span></span></span></span></td>
<td style="text-align:center">+</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>−</mo></mrow><annotation encoding="application/x-tex">-</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">−</span></span></span></span></td>
<td style="text-align:center">-</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>×</mo></mrow><annotation encoding="application/x-tex">\times</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">×</span></span></span></span></td>
<td style="text-align:center">\times</td>
</tr>
<tr>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>±</mo></mrow><annotation encoding="application/x-tex">\pm</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">±</span></span></span></span></td>
<td style="text-align:center">\pm</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>⋅</mo></mrow><annotation encoding="application/x-tex">\cdot</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4445em;"></span><span class="mord">⋅</span></span></span></span></td>
<td style="text-align:center">\cdot</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>∗</mo></mrow><annotation encoding="application/x-tex">\ast</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4653em;"></span><span class="mord">∗</span></span></span></span></td>
<td style="text-align:center">\ast</td>
</tr>
<tr>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>∪</mo></mrow><annotation encoding="application/x-tex">\cup</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5556em;"></span><span class="mord">∪</span></span></span></span></td>
<td style="text-align:center">\cup</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>∩</mo></mrow><annotation encoding="application/x-tex">\cap</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5556em;"></span><span class="mord">∩</span></span></span></span></td>
<td style="text-align:center">\cap</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>∘</mo></mrow><annotation encoding="application/x-tex">\circ</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4445em;"></span><span class="mord">∘</span></span></span></span></td>
<td style="text-align:center">\circ</td>
</tr>
<tr>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>∨</mo></mrow><annotation encoding="application/x-tex">\lor</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5556em;"></span><span class="mord">∨</span></span></span></span></td>
<td style="text-align:center">\lor</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>∧</mo></mrow><annotation encoding="application/x-tex">\land</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5556em;"></span><span class="mord">∧</span></span></span></span></td>
<td style="text-align:center">\land</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">¬</mi></mrow><annotation encoding="application/x-tex">\lnot</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord">¬</span></span></span></span></td>
<td style="text-align:center">\lnot</td>
</tr>
<tr>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>⊕</mo></mrow><annotation encoding="application/x-tex">\oplus</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">⊕</span></span></span></span></td>
<td style="text-align:center">\oplus</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>⊖</mo></mrow><annotation encoding="application/x-tex">\ominus</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">⊖</span></span></span></span></td>
<td style="text-align:center">\ominus</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>⊗</mo></mrow><annotation encoding="application/x-tex">\otimes</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">⊗</span></span></span></span></td>
<td style="text-align:center">\otimes</td>
</tr>
<tr>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>⊙</mo></mrow><annotation encoding="application/x-tex">\odot</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">⊙</span></span></span></span></td>
<td style="text-align:center">\odot</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>⊘</mo></mrow><annotation encoding="application/x-tex">\oslash</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">⊘</span></span></span></span></td>
<td style="text-align:center">\oslash</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>∙</mo></mrow><annotation encoding="application/x-tex">\bullet</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4445em;"></span><span class="mord">∙</span></span></span></span></td>
<td style="text-align:center">\bullet</td>
</tr>
<tr>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msqrt><mi>x</mi></msqrt><mi>x</mi></mrow><annotation encoding="application/x-tex">\sqrt{x}x</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.04em;vertical-align:-0.2397em;"></span><span class="mord sqrt"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8003em;"><span class="svg-align" style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style="padding-left:0.833em;"><span class="mord mathnormal">x</span></span></span><span style="top:-2.7603em;"><span class="pstrut" style="height:3em;"></span><span class="hide-tail" style="min-width:0.853em;height:1.08em;"><svg xmlns="http://www.w3.org/2000/svg" width='400em' height='1.08em' viewBox='0 0 400000 1080' preserveAspectRatio='xMinYMin slice'><path d='M95,702
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c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54
c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10
s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429
c69,-144,104.5,-217.7,106.5,-221
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c5.3,-9.3,12,-14,20,-14
H400000v40H845.2724
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M834 80h400000v40h-400000z'/></svg></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2397em;"><span></span></span></span></span></span><span class="mord mathnormal">x</span></span></span></span></td>
<td style="text-align:center">\sqrt{x}x</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mroot><mi>x</mi><mi>n</mi></mroot><mi>n</mi><mi>x</mi></mrow><annotation encoding="application/x-tex">\sqrt[n]{x}nx</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.04em;vertical-align:-0.2397em;"></span><span class="mord sqrt"><span class="root"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.5516em;"><span style="top:-2.8363em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size6 size1 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">n</span></span></span></span></span></span></span></span><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8003em;"><span class="svg-align" style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style="padding-left:0.833em;"><span class="mord mathnormal">x</span></span></span><span style="top:-2.7603em;"><span class="pstrut" style="height:3em;"></span><span class="hide-tail" style="min-width:0.853em;height:1.08em;"><svg xmlns="http://www.w3.org/2000/svg" width='400em' height='1.08em' viewBox='0 0 400000 1080' preserveAspectRatio='xMinYMin slice'><path d='M95,702
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c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54
c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10
s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429
c69,-144,104.5,-217.7,106.5,-221
l0 -0
c5.3,-9.3,12,-14,20,-14
H400000v40H845.2724
s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7
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M834 80h400000v40h-400000z'/></svg></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2397em;"><span></span></span></span></span></span><span class="mord mathnormal">n</span><span class="mord mathnormal">x</span></span></span></span></td>
<td style="text-align:center">\sqrt[n]{x}nx</td>
<td style="text-align:center"></td>
<td style="text-align:center"></td>
</tr>
</tbody>
</table>
<h3 id="大尺寸运算符">大尺寸运算符</h3>
<table>
<thead>
<tr>
<th style="text-align:center">运算符</th>
<th style="text-align:center">语法</th>
<th style="text-align:center">运算符</th>
<th style="text-align:center">语法</th>
<th style="text-align:center">运算符</th>
<th style="text-align:center">语法</th>
</tr>
</thead>
<tbody>
<tr>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>∑</mo></mrow><annotation encoding="application/x-tex">\sum</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mop op-symbol small-op" style="position:relative;top:0em;">∑</span></span></span></span></td>
<td style="text-align:center">\sum</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>∏</mo></mrow><annotation encoding="application/x-tex">\prod</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mop op-symbol small-op" style="position:relative;top:0em;">∏</span></span></span></span></td>
<td style="text-align:center">\prod</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>∫</mo></mrow><annotation encoding="application/x-tex">\int</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.1111em;vertical-align:-0.3061em;"></span><span class="mop op-symbol small-op" style="margin-right:0.19445em;position:relative;top:-0.0006em;">∫</span></span></span></span></td>
<td style="text-align:center">\int</td>
</tr>
<tr>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>⋃</mo></mrow><annotation encoding="application/x-tex">\bigcup</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mop op-symbol small-op" style="position:relative;top:0em;">⋃</span></span></span></span></td>
<td style="text-align:center">\bigcup</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>⋂</mo></mrow><annotation encoding="application/x-tex">\bigcap</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mop op-symbol small-op" style="position:relative;top:0em;">⋂</span></span></span></span></td>
<td style="text-align:center">\bigcap</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>∮</mo></mrow><annotation encoding="application/x-tex">\oint</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.1111em;vertical-align:-0.3061em;"></span><span class="mop op-symbol small-op" style="margin-right:0.19445em;position:relative;top:-0.0006em;">∮</span></span></span></span></td>
<td style="text-align:center">\oint</td>
</tr>
<tr>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>⋁</mo></mrow><annotation encoding="application/x-tex">\bigvee</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mop op-symbol small-op" style="position:relative;top:0em;">⋁</span></span></span></span></td>
<td style="text-align:center">\bigvee</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>⋀</mo></mrow><annotation encoding="application/x-tex">\bigwedge</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mop op-symbol small-op" style="position:relative;top:0em;">⋀</span></span></span></span></td>
<td style="text-align:center">\bigwedge</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>∬</mo></mrow><annotation encoding="application/x-tex">\iint</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.111em;vertical-align:-0.306em;"></span><span class="mop op-symbol small-op" style="margin-right:0.19445em;position:relative;top:-0.0005em;">∬</span></span></span></span></td>
<td style="text-align:center">\iint</td>
</tr>
<tr>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>∐</mo></mrow><annotation encoding="application/x-tex">\coprod</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mop op-symbol small-op" style="position:relative;top:0em;">∐</span></span></span></span></td>
<td style="text-align:center">\coprod</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>⨆</mo></mrow><annotation encoding="application/x-tex">\bigsqcup</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mop op-symbol small-op" style="position:relative;top:0em;">⨆</span></span></span></span></td>
<td style="text-align:center">\bigsqcup</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>∯</mo></mrow><annotation encoding="application/x-tex">\oiint</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.111em;vertical-align:-0.306em;"></span><span class="mop vlist-t vlist-t2" style="position:relative;top:-0.0005em;"><span class="vlist-r"><span class="vlist" style="height:0.805em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mop op-symbol small-op" style="margin-right:0.19445em;">∬</span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="overlay" style="height:0.499em;width:0.957em;"><svg xmlns="http://www.w3.org/2000/svg" width='0.957em' height='0.499em' style='width:0.957em' viewBox='0 0 957 499' preserveAspectRatio='xMinYMin'><path d='M512.6 71.6c272.6 0 320.3 106.8 320.3 178.2 0 70.8-47.7 177.6
-320.3 177.6S193.1 320.6 193.1 249.8c0-71.4 46.9-178.2 319.5-178.2z
m368.1 178.2c0-86.4-60.9-215.4-368.1-215.4-306.4 0-367.3 129-367.3 215.4 0 85.8
60.9 214.8 367.3 214.8 307.2 0 368.1-129 368.1-214.8z'/></svg></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.306em;"><span></span></span></span></span></span></span></span></td>
<td style="text-align:center">\oiint</td>
</tr>
</tbody>
</table>
<h3 id="常见关系符号">常见关系符号</h3>
<table>
<thead>
<tr>
<th style="text-align:center">符号</th>
<th style="text-align:center">语法</th>
<th style="text-align:center">符号</th>
<th style="text-align:center">语法</th>
<th style="text-align:center">符号</th>
<th style="text-align:center">语法</th>
</tr>
</thead>
<tbody>
<tr>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>≤</mo></mrow><annotation encoding="application/x-tex">\leq</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7719em;vertical-align:-0.136em;"></span><span class="mrel">≤</span></span></span></span></td>
<td style="text-align:center">\leq</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>≥</mo></mrow><annotation encoding="application/x-tex">\geq</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7719em;vertical-align:-0.136em;"></span><span class="mrel">≥</span></span></span></span></td>
<td style="text-align:center">\geq</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo mathvariant="normal">≠</mo><mspace linebreak="newline"></mspace></mrow><annotation encoding="application/x-tex">\neq\\</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mrel"><span class="mrel"><span class="mord vbox"><span class="thinbox"><span class="rlap"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="inner"><span class="mord"><span class="mrel"></span></span></span><span class="fix"></span></span></span></span></span><span class="mrel">=</span></span></span><span class="mspace newline"></span></span></span></td>
<td style="text-align:center">\neq\</td>
</tr>
<tr>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>≪</mo></mrow><annotation encoding="application/x-tex">\ll</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5782em;vertical-align:-0.0391em;"></span><span class="mrel">≪</span></span></span></span></td>
<td style="text-align:center">\ll</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>≫</mo></mrow><annotation encoding="application/x-tex">\gg</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5782em;vertical-align:-0.0391em;"></span><span class="mrel">≫</span></span></span></span></td>
<td style="text-align:center">\gg</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>≡</mo></mrow><annotation encoding="application/x-tex">\equiv</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4637em;"></span><span class="mrel">≡</span></span></span></span></td>
<td style="text-align:center">\equiv</td>
</tr>
<tr>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>⊂</mo></mrow><annotation encoding="application/x-tex">\subset</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5782em;vertical-align:-0.0391em;"></span><span class="mrel">⊂</span></span></span></span></td>
<td style="text-align:center">\subset</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>⊃</mo></mrow><annotation encoding="application/x-tex">\supset</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5782em;vertical-align:-0.0391em;"></span><span class="mrel">⊃</span></span></span></span></td>
<td style="text-align:center">\supset</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>≈</mo></mrow><annotation encoding="application/x-tex">\approx</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4831em;"></span><span class="mrel">≈</span></span></span></span></td>
<td style="text-align:center">\approx</td>
</tr>
<tr>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>⊆</mo></mrow><annotation encoding="application/x-tex">\subseteq</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7719em;vertical-align:-0.136em;"></span><span class="mrel">⊆</span></span></span></span></td>
<td style="text-align:center">\subseteq</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>⊇</mo></mrow><annotation encoding="application/x-tex">\supseteq</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7719em;vertical-align:-0.136em;"></span><span class="mrel">⊇</span></span></span></span></td>
<td style="text-align:center">\supseteq</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>∼</mo></mrow><annotation encoding="application/x-tex">\sim</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.3669em;"></span><span class="mrel">∼</span></span></span></span></td>
<td style="text-align:center">\sim</td>
</tr>
<tr>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>∈</mo></mrow><annotation encoding="application/x-tex">\in</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5782em;vertical-align:-0.0391em;"></span><span class="mrel">∈</span></span></span></span></td>
<td style="text-align:center">\in</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>n</mi><mi>i</mi></mrow><annotation encoding="application/x-tex">ni</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6595em;"></span><span class="mord mathnormal">ni</span></span></span></span></td>
<td style="text-align:center">\ni</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>∝</mo></mrow><annotation encoding="application/x-tex">\propto</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mrel">∝</span></span></span></span></td>
<td style="text-align:center">\propto</td>
</tr>
<tr>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>⊢</mo></mrow><annotation encoding="application/x-tex">\vdash</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mrel">⊢</span></span></span></span></td>
<td style="text-align:center">\vdash</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>⊣</mo></mrow><annotation encoding="application/x-tex">\dashv</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mrel">⊣</span></span></span></span></td>
<td style="text-align:center">\dashv</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>⊨</mo></mrow><annotation encoding="application/x-tex">\models</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.999em;vertical-align:-0.249em;"></span><span class="mrel">⊨</span></span></span></span></td>
<td style="text-align:center">\models</td>
</tr>
<tr>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>∣</mo></mrow><annotation encoding="application/x-tex">\mid</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mrel">∣</span></span></span></span></td>
<td style="text-align:center">\mid</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>∥</mo></mrow><annotation encoding="application/x-tex">\parallel</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mrel">∥</span></span></span></span></td>
<td style="text-align:center">\parallel</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>⊥</mo></mrow><annotation encoding="application/x-tex">\perp</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mrel">⊥</span></span></span></span></td>
<td style="text-align:center">\perp</td>
</tr>
<tr>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo mathvariant="normal">∉</mo></mrow><annotation encoding="application/x-tex">\notin</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mrel"><span class="mord"><span class="mrel">∈</span></span><span class="mord vbox"><span class="thinbox"><span class="llap"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="inner"><span class="mord"><span class="mord">/</span><span class="mspace" style="margin-right:0.0556em;"></span></span></span><span class="fix"></span></span></span></span></span></span></span></span></td>
<td style="text-align:center">\notin</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>⋈</mo></mrow><annotation encoding="application/x-tex">\Join</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.51em;vertical-align:-0.005em;"></span><span class="mrel">⋈</span></span></span></span></td>
<td style="text-align:center">\Join</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>≁</mo></mrow><annotation encoding="application/x-tex">\nsim</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.3669em;"></span><span class="mrel amsrm">≁</span></span></span></span></td>
<td style="text-align:center">\nsim</td>
</tr>
<tr>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>⊊</mo></mrow><annotation encoding="application/x-tex">\subsetneq</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7719em;vertical-align:-0.136em;"></span><span class="mrel amsrm">⊊</span></span></span></span></td>
<td style="text-align:center">\subsetneq</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>⊋</mo></mrow><annotation encoding="application/x-tex">\supsetneq</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7719em;vertical-align:-0.136em;"></span><span class="mrel amsrm">⊋</span></span></span></span></td>
<td style="text-align:center">\supsetneq</td>
<td style="text-align:center"></td>
<td style="text-align:center"></td>
</tr>
</tbody>
</table>
<h3 id="数学模式重音符">数学模式重音符</h3>
<table>
<thead>
<tr>
<th style="text-align:center">符号</th>
<th style="text-align:center">语法</th>
<th style="text-align:center">符号</th>
<th style="text-align:center">语法</th>
<th style="text-align:center">符号</th>
<th style="text-align:center">语法</th>
</tr>
</thead>
<tbody>
<tr>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mover accent="true"><mi>a</mi><mo>^</mo></mover><mi>a</mi></mrow><annotation encoding="application/x-tex">\hat{a}a</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6944em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mathnormal">a</span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord">^</span></span></span></span></span></span></span><span class="mord mathnormal">a</span></span></span></span></td>
<td style="text-align:center">\hat{a}a</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mover accent="true"><mi>a</mi><mo>ˉ</mo></mover><mi>a</mi></mrow><annotation encoding="application/x-tex">\bar{a}a</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5678em;"></span><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.5678em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mathnormal">a</span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord">ˉ</span></span></span></span></span></span></span><span class="mord mathnormal">a</span></span></span></span></td>
<td style="text-align:center">\bar{a}a</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mover accent="true"><mi>a</mi><mo>~</mo></mover><mi>a</mi></mrow><annotation encoding="application/x-tex">\tilde{a}a</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6679em;"></span><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6679em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mathnormal">a</span></span><span style="top:-3.35em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord">~</span></span></span></span></span></span></span><span class="mord mathnormal">a</span></span></span></span></td>
<td style="text-align:center">\tilde{a}a</td>
</tr>
<tr>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mover accent="true"><mi>a</mi><mo>⃗</mo></mover></mrow><annotation encoding="application/x-tex">\vec{a}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.714em;"></span><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.714em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mathnormal">a</span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.2355em;"><span class="overlay" style="height:0.714em;width:0.471em;"><svg xmlns="http://www.w3.org/2000/svg" width='0.471em' height='0.714em' style='width:0.471em' viewBox='0 0 471 714' preserveAspectRatio='xMinYMin'><path d='M377 20c0-5.333 1.833-10 5.5-14S391 0 397 0c4.667 0 8.667 1.667 12 5
3.333 2.667 6.667 9 10 19 6.667 24.667 20.333 43.667 41 57 7.333 4.667 11
10.667 11 18 0 6-1 10-3 12s-6.667 5-14 9c-28.667 14.667-53.667 35.667-75 63
-1.333 1.333-3.167 3.5-5.5 6.5s-4 4.833-5 5.5c-1 .667-2.5 1.333-4.5 2s-4.333 1
-7 1c-4.667 0-9.167-1.833-13.5-5.5S337 184 337 178c0-12.667 15.667-32.333 47-59
H213l-171-1c-8.667-6-13-12.333-13-19 0-4.667 4.333-11.333 13-20h359
c-16-25.333-24-45-24-59z'/></svg></span></span></span></span></span></span></span></span></span></span></td>
<td style="text-align:center">\vec{a}</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mover accent="true"><mi>a</mi><mo>˙</mo></mover><mi>a</mi></mrow><annotation encoding="application/x-tex">\dot{a}a</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6679em;"></span><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6679em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mathnormal">a</span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.1389em;"><span class="mord">˙</span></span></span></span></span></span></span><span class="mord mathnormal">a</span></span></span></span></td>
<td style="text-align:center">\dot{a}a</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mover accent="true"><mi>a</mi><mo>¨</mo></mover><mi>a</mi></mrow><annotation encoding="application/x-tex">\ddot{a}a</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6679em;"></span><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6679em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mathnormal">a</span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.25em;"><span class="mord">¨</span></span></span></span></span></span></span><span class="mord mathnormal">a</span></span></span></span></td>
<td style="text-align:center">\ddot{a}a</td>
</tr>
<tr>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mover accent="true"><mrow><mi>a</mi><mi>b</mi><mi>c</mi></mrow><mo stretchy="true">^</mo></mover><mi>a</mi><mi>b</mi></mrow><annotation encoding="application/x-tex">\widehat{abc}ab</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.9944em;"></span><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9944em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">ab</span><span class="mord mathnormal">c</span></span></span><span class="svg-align" style="top:-3.6944em;"><span class="pstrut" style="height:3em;"></span><span style="height:0.3em;"><svg xmlns="http://www.w3.org/2000/svg" width='100%' height='0.3em' viewBox='0 0 2364 300' preserveAspectRatio='none'><path d='M1181 0h2l1171 176c6 0 10 5 10 11l-2 23c-1 6-5 10
-11 10h-1L1182 67 15 220h-1c-6 0-10-4-11-10l-2-23c-1-6 4-11 10-11z'/></svg></span></span></span></span></span></span><span class="mord mathnormal">ab</span></span></span></span></td>
<td style="text-align:center">\widehat{abc}ab</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mover accent="true"><mrow><mi>a</mi><mi>b</mi><mi>c</mi></mrow><mo stretchy="true">~</mo></mover><mi>a</mi><mi>b</mi></mrow><annotation encoding="application/x-tex">\widetilde{abc}ab</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.9804em;"></span><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9804em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">ab</span><span class="mord mathnormal">c</span></span></span><span class="svg-align" style="top:-3.6944em;"><span class="pstrut" style="height:3em;"></span><span style="height:0.286em;"><svg xmlns="http://www.w3.org/2000/svg" width='100%' height='0.286em' viewBox='0 0 1033 286' preserveAspectRatio='none'><path d='M344 55.266c-142 0-300.638 81.316-311.5 86.418
-8.01 3.762-22.5 10.91-23.5 5.562L1 120c-1-2-1-3-1-4 0-5 3-9 8-10l18.4-9C160.9
 31.9 283 0 358 0c148 0 188 122 331 122s314-97 326-97c4 0 8 2 10 7l7 21.114
c1 2.14 1 3.21 1 4.28 0 5.347-3 9.626-7 10.696l-22.3 12.622C852.6 158.372 751
 181.476 676 181.476c-149 0-189-126.21-332-126.21z'/></svg></span></span></span></span></span></span><span class="mord mathnormal">ab</span></span></span></span></td>
<td style="text-align:center">\widetilde{abc}ab</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mover accent="true"><mrow><mi>a</mi><mi>b</mi><mi>c</mi></mrow><mo stretchy="true">‾</mo></mover><mi>a</mi><mi>b</mi></mrow><annotation encoding="application/x-tex">\overline{abc}ab</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8944em;"></span><span class="mord overline"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8944em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">ab</span><span class="mord mathnormal">c</span></span></span><span style="top:-3.8144em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span></span></span></span><span class="mord mathnormal">ab</span></span></span></span></td>
<td style="text-align:center">\overline{abc}ab</td>
</tr>
</tbody>
</table>
<h3 id="箭头">箭头</h3>
<p>如果需要长箭头，只需要在语法前面加上<code>\long</code>，例如<code>\longleftarrow</code>即为<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>⟵</mo></mrow><annotation encoding="application/x-tex">\longleftarrow</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.522em;vertical-align:-0.011em;"></span><span class="mrel">⟵</span></span></span></span>，如果加上<code>\Long</code>则变为双线长箭头，例如<code>\Longleftarrow</code>即为<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>⟸</mo></mrow><annotation encoding="application/x-tex">\Longleftarrow</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.549em;vertical-align:-0.024em;"></span><span class="mrel">⟸</span></span></span></span></p>
<table>
<thead>
<tr>
<th style="text-align:center">符号</th>
<th style="text-align:center">语法</th>
<th style="text-align:center">符号</th>
<th style="text-align:center">语法</th>
<th style="text-align:center">符号</th>
<th style="text-align:center">语法</th>
</tr>
</thead>
<tbody>
<tr>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>←</mo></mrow><annotation encoding="application/x-tex">\leftarrow</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.3669em;"></span><span class="mrel">←</span></span></span></span></td>
<td style="text-align:center">\leftarrow</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>→</mo></mrow><annotation encoding="application/x-tex">\rightarrow</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.3669em;"></span><span class="mrel">→</span></span></span></span></td>
<td style="text-align:center">\rightarrow</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>↔</mo></mrow><annotation encoding="application/x-tex">\leftrightarrow</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.3669em;"></span><span class="mrel">↔</span></span></span></span></td>
<td style="text-align:center">\leftrightarrow</td>
</tr>
<tr>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>⇐</mo></mrow><annotation encoding="application/x-tex">\Leftarrow</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.3669em;"></span><span class="mrel">⇐</span></span></span></span></td>
<td style="text-align:center">\Leftarrow</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>⇒</mo></mrow><annotation encoding="application/x-tex">\Rightarrow</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.3669em;"></span><span class="mrel">⇒</span></span></span></span></td>
<td style="text-align:center">\Rightarrow</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>⇔</mo></mrow><annotation encoding="application/x-tex">\Leftrightarrow</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.3669em;"></span><span class="mrel">⇔</span></span></span></span></td>
<td style="text-align:center">\Leftrightarrow</td>
</tr>
<tr>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>↑</mo></mrow><annotation encoding="application/x-tex">\uparrow</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mrel">↑</span></span></span></span></td>
<td style="text-align:center">\uparrow</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>↓</mo></mrow><annotation encoding="application/x-tex">\downarrow</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mrel">↓</span></span></span></span></td>
<td style="text-align:center">\downarrow</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>↕</mo></mrow><annotation encoding="application/x-tex">\updownarrow</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mrel">↕</span></span></span></span></td>
<td style="text-align:center">\updownarrow</td>
</tr>
<tr>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>⇑</mo></mrow><annotation encoding="application/x-tex">\Uparrow</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mrel">⇑</span></span></span></span></td>
<td style="text-align:center">\Uparrow</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>⇓</mo></mrow><annotation encoding="application/x-tex">\Downarrow</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mrel">⇓</span></span></span></span></td>
<td style="text-align:center">\Downarrow</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>⇕</mo></mrow><annotation encoding="application/x-tex">\Updownarrow</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mrel">⇕</span></span></span></span></td>
<td style="text-align:center">\Updownarrow</td>
</tr>
<tr>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>↼</mo></mrow><annotation encoding="application/x-tex">\leftharpoonup</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.3669em;"></span><span class="mrel">↼</span></span></span></span></td>
<td style="text-align:center">\leftharpoonup</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>↽</mo></mrow><annotation encoding="application/x-tex">\leftharpoondown</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.3669em;"></span><span class="mrel">↽</span></span></span></span></td>
<td style="text-align:center">\leftharpoondown</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>⇀</mo></mrow><annotation encoding="application/x-tex">\rightharpoonup</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.3669em;"></span><span class="mrel">⇀</span></span></span></span></td>
<td style="text-align:center">\rightharpoonup</td>
</tr>
<tr>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>⇁</mo></mrow><annotation encoding="application/x-tex">\rightharpoondown</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.3669em;"></span><span class="mrel">⇁</span></span></span></span></td>
<td style="text-align:center">\rightharpoondown</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>⇌</mo></mrow><annotation encoding="application/x-tex">\rightleftharpoons</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.682em;vertical-align:-0.011em;"></span><span class="mrel">⇌</span></span></span></span></td>
<td style="text-align:center">\rightleftharpoons</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>⇋</mo></mrow><annotation encoding="application/x-tex">\leftrightharpoons</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5359em;vertical-align:-0.0135em;"></span><span class="mrel amsrm">⇋</span></span></span></span></td>
<td style="text-align:center">\leftrightharpoons</td>
</tr>
<tr>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mtext>  </mtext><mo>⟺</mo><mtext>  </mtext></mrow><annotation encoding="application/x-tex">\iff</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.549em;vertical-align:-0.024em;"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">⟺</span><span class="mspace" style="margin-right:0.2778em;"></span></span></span></span></td>
<td style="text-align:center">\iff</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>↦</mo></mrow><annotation encoding="application/x-tex">\mapsto</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.522em;vertical-align:-0.011em;"></span><span class="mrel">↦</span></span></span></span></td>
<td style="text-align:center">\mapsto</td>
<td style="text-align:center"></td>
<td style="text-align:center"></td>
</tr>
</tbody>
</table>
<h3 id="括号">括号</h3>
<table>
<thead>
<tr>
<th style="text-align:center">括号</th>
<th style="text-align:center">语法</th>
<th style="text-align:center">括号</th>
<th style="text-align:center">语法</th>
<th style="text-align:center">括号</th>
<th style="text-align:center">语法</th>
</tr>
</thead>
<tbody>
<tr>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">()</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mclose">)</span></span></span></span></td>
<td style="text-align:center">()</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">[</mo><mo stretchy="false">]</mo></mrow><annotation encoding="application/x-tex">[]</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">[</span><span class="mclose">]</span></span></span></span></td>
<td style="text-align:center">[]</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">{</mo><mo stretchy="false">}</mo></mrow><annotation encoding="application/x-tex">\{\}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">{</span><span class="mclose">}</span></span></span></span></td>
<td style="text-align:center">{}</td>
</tr>
<tr>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">⌊</mo><mo stretchy="false">⌋</mo></mrow><annotation encoding="application/x-tex">\lfloor\rfloor</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">⌊</span><span class="mclose">⌋</span></span></span></span></td>
<td style="text-align:center">\lfloor\rfloor</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">⌈</mo><mo stretchy="false">⌉</mo></mrow><annotation encoding="application/x-tex">\lceil\rceil</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">⌈</span><span class="mclose">⌉</span></span></span></span></td>
<td style="text-align:center">\lceil\rceil</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">⟨</mo><mo stretchy="false">⟩</mo></mrow><annotation encoding="application/x-tex">\langle\rangle</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">⟨</span><span class="mclose">⟩</span></span></span></span></td>
<td style="text-align:center">\langle\rangle</td>
</tr>
</tbody>
</table>
<h3 id="大尺寸括号">大尺寸括号</h3>
<table>
<thead>
<tr>
<th style="text-align:center">括号</th>
<th style="text-align:center">语法</th>
<th style="text-align:center">括号</th>
<th style="text-align:center">语法</th>
</tr>
</thead>
<tbody>
<tr>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo fence="true">(</mo><mo fence="true">)</mo></mrow><annotation encoding="application/x-tex">\left( \right)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;">(</span><span class="mclose delimcenter" style="top:0em;">)</span></span></span></span></span></td>
<td style="text-align:center">\left( \right)</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo fence="true">[</mo><mo fence="true">]</mo></mrow><annotation encoding="application/x-tex">\left[ \right]</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;">[</span><span class="mclose delimcenter" style="top:0em;">]</span></span></span></span></span></td>
<td style="text-align:center">\left[ \right]</td>
</tr>
<tr>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mover><mover><mrow><msub><mi>x</mi><mn>1</mn></msub><msub><mi>x</mi><mn>2</mn></msub><mo>…</mo><msub><mi>x</mi><mi>n</mi></msub></mrow><mo stretchy="true">⏞</mo></mover><mi>n</mi></mover></mrow><annotation encoding="application/x-tex">\overbrace{x_1x_2\ldots x_n}^{n}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.73em;vertical-align:-0.15em;"></span><span class="mord mover"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.58em;"><span style="top:-3.0786em;"><span class="pstrut" style="height:3.0786em;"></span><span class="mord mover"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.0786em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner">…</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span><span class="svg-align" style="top:-3.5306em;"><span class="pstrut" style="height:3em;"></span><span class="stretchy" style="height:0.548em;min-width:1.6em;"><span class="brace-left" style="height:0.548em;"><svg xmlns="http://www.w3.org/2000/svg" width='400em' height='0.548em' viewBox='0 0 400000 548' preserveAspectRatio='xMinYMin slice'><path d='M6 548l-6-6v-35l6-11c56-104 135.3-181.3 238-232 57.3-28.7 117
-45 179-50h399577v120H403c-43.3 7-81 15-113 26-100.7 33-179.7 91-237 174-2.7
 5-6 9-10 13-.7 1-7.3 1-20 1H6z'/></svg></span><span class="brace-center" style="height:0.548em;"><svg xmlns="http://www.w3.org/2000/svg" width='400em' height='0.548em' viewBox='0 0 400000 548' preserveAspectRatio='xMidYMin slice'><path d='M200428 334
c-100.7-8.3-195.3-44-280-108-55.3-42-101.7-93-139-153l-9-14c-2.7 4-5.7 8.7-9 14
-53.3 86.7-123.7 153-211 199-66.7 36-137.3 56.3-212 62H0V214h199568c178.3-11.7
 311.7-78.3 403-201 6-8 9.7-12 11-12 .7-.7 6.7-1 18-1s17.3.3 18 1c1.3 0 5 4 11
 12 44.7 59.3 101.3 106.3 170 141s145.3 54.3 229 60h199572v120z'/></svg></span><span class="brace-right" style="height:0.548em;"><svg xmlns="http://www.w3.org/2000/svg" width='400em' height='0.548em' viewBox='0 0 400000 548' preserveAspectRatio='xMaxYMin slice'><path d='M400000 542l
-6 6h-17c-12.7 0-19.3-.3-20-1-4-4-7.3-8.3-10-13-35.3-51.3-80.8-93.8-136.5-127.5
s-117.2-55.8-184.5-66.5c-.7 0-2-.3-4-1-18.7-2.7-76-4.3-172-5H0V214h399571l6 1
c124.7 8 235 61.7 331 161 31.3 33.3 59.7 72.7 85 118l7 13v35z'/></svg></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span style="top:-4.3571em;"><span class="pstrut" style="height:3.0786em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">n</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></td>
<td style="text-align:center">\overbrace{x_1x_2\ldots x_n}^{n}</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><munder><munder><mrow><msub><mi>x</mi><mn>1</mn></msub><msub><mi>x</mi><mn>2</mn></msub><mo>…</mo><msub><mi>x</mi><mi>n</mi></msub></mrow><mo stretchy="true">⏟</mo></munder><mi>n</mi></munder></mrow><annotation encoding="application/x-tex">\underbrace{x_1x_2\ldots x_n}_{n}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.73em;vertical-align:-1.2994em;"></span><span class="mord munder"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.4306em;"><span style="top:-1.7006em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord munder"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.4306em;"><span class="svg-align" style="top:-2.202em;"><span class="pstrut" style="height:3em;"></span><span class="stretchy" style="height:0.548em;min-width:1.6em;"><span class="brace-left" style="height:0.548em;"><svg xmlns="http://www.w3.org/2000/svg" width='400em' height='0.548em' viewBox='0 0 400000 548' preserveAspectRatio='xMinYMin slice'><path d='M0 6l6-6h17c12.688 0 19.313.3 20 1 4 4 7.313 8.3 10 13
 35.313 51.3 80.813 93.8 136.5 127.5 55.688 33.7 117.188 55.8 184.5 66.5.688
 0 2 .3 4 1 18.688 2.7 76 4.3 172 5h399450v120H429l-6-1c-124.688-8-235-61.7
-331-161C60.687 138.7 32.312 99.3 7 54L0 41V6z'/></svg></span><span class="brace-center" style="height:0.548em;"><svg xmlns="http://www.w3.org/2000/svg" width='400em' height='0.548em' viewBox='0 0 400000 548' preserveAspectRatio='xMidYMin slice'><path d='M199572 214
c100.7 8.3 195.3 44 280 108 55.3 42 101.7 93 139 153l9 14c2.7-4 5.7-8.7 9-14
 53.3-86.7 123.7-153 211-199 66.7-36 137.3-56.3 212-62h199568v120H200432c-178.3
 11.7-311.7 78.3-403 201-6 8-9.7 12-11 12-.7.7-6.7 1-18 1s-17.3-.3-18-1c-1.3 0
-5-4-11-12-44.7-59.3-101.3-106.3-170-141s-145.3-54.3-229-60H0V214z'/></svg></span><span class="brace-right" style="height:0.548em;"><svg xmlns="http://www.w3.org/2000/svg" width='400em' height='0.548em' viewBox='0 0 400000 548' preserveAspectRatio='xMaxYMin slice'><path d='M399994 0l6 6v35l-6 11c-56 104-135.3 181.3-238 232-57.3
 28.7-117 45-179 50H-300V214h399897c43.3-7 81-15 113-26 100.7-33 179.7-91 237
-174 2.7-5 6-9 10-13 .7-1 7.3-1 20-1h17z'/></svg></span></span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner">…</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.798em;"><span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.2994em;"><span></span></span></span></span></span></span></span></span></td>
<td style="text-align:center">\underbrace{x_1x_2\ldots x_n}_{n}</td>
</tr>
</tbody>
</table>
<p><strong>注：大尺寸的()和[]是可以根据公式的高度自动调节的，例如</strong></p>
<figure class="highlight dust"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br></pre></td><td class="code"><pre><span class="line"><span class="language-xml">\arg\min_</span><span class="template-variable">&#123;\theta&#125;</span><span class="language-xml"></span></span><br><span class="line"><span class="language-xml">\left[</span></span><br><span class="line"><span class="language-xml">    -\sum_</span><span class="template-variable">&#123;i=1&#125;</span><span class="language-xml">^</span><span class="template-variable">&#123;n&#125;</span><span class="language-xml"></span></span><br><span class="line"><span class="language-xml">    \left[</span></span><br><span class="line"><span class="language-xml">        \mathbf</span><span class="template-variable">&#123;y&#125;</span><span class="language-xml">^</span><span class="template-variable">&#123;(i)&#125;</span><span class="language-xml">\ln(h_</span><span class="template-variable">&#123;\theta&#125;</span><span class="language-xml">(\mathbf</span><span class="template-variable">&#123;x&#125;</span><span class="language-xml">^</span><span class="template-variable">&#123;(i)&#125;</span><span class="language-xml">)) +</span></span><br><span class="line"><span class="language-xml">        (1-\mathbf</span><span class="template-variable">&#123;y&#125;</span><span class="language-xml">^</span><span class="template-variable">&#123;(i)&#125;</span><span class="language-xml">)\ln(1-h_</span><span class="template-variable">&#123;\theta&#125;</span><span class="language-xml">(\mathbf</span><span class="template-variable">&#123;x&#125;</span><span class="language-xml">^</span><span class="template-variable">&#123;(i)&#125;</span><span class="language-xml">))</span></span><br><span class="line"><span class="language-xml">    \right]</span></span><br><span class="line"><span class="language-xml">\right]</span></span><br></pre></td></tr></table></figure>
<p><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>arg</mi><mo>⁡</mo><munder><mrow><mi>min</mi><mo>⁡</mo></mrow><mi>θ</mi></munder><mrow><mo fence="true">[</mo><mo>−</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></munderover><mrow><mo fence="true">[</mo><msup><mi mathvariant="bold">y</mi><mrow><mo stretchy="false">(</mo><mi>i</mi><mo stretchy="false">)</mo></mrow></msup><mi>ln</mi><mo>⁡</mo><mo stretchy="false">(</mo><msub><mi>h</mi><mi>θ</mi></msub><mo stretchy="false">(</mo><msup><mi mathvariant="bold">x</mi><mrow><mo stretchy="false">(</mo><mi>i</mi><mo stretchy="false">)</mo></mrow></msup><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo>+</mo><mo stretchy="false">(</mo><mn>1</mn><mo>−</mo><msup><mi mathvariant="bold">y</mi><mrow><mo stretchy="false">(</mo><mi>i</mi><mo stretchy="false">)</mo></mrow></msup><mo stretchy="false">)</mo><mi>ln</mi><mo>⁡</mo><mo stretchy="false">(</mo><mn>1</mn><mo>−</mo><msub><mi>h</mi><mi>θ</mi></msub><mo stretchy="false">(</mo><msup><mi mathvariant="bold">x</mi><mrow><mo stretchy="false">(</mo><mi>i</mi><mo stretchy="false">)</mo></mrow></msup><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo fence="true">]</mo></mrow><mo fence="true">]</mo></mrow></mrow><annotation encoding="application/x-tex">\arg\min_{\theta} \left[ -\sum_{i=1}^{n} \left[ \mathbf{y}^{(i)}\ln(h_{\theta}(\mathbf{x}^{(i)})) + (1-\mathbf{y}^{(i)})\ln(1-h_{\theta}(\mathbf{x}^{(i)})) \right] \right]
</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:3.0277em;vertical-align:-1.2777em;"></span><span class="mop">ar<span style="margin-right:0.01389em;">g</span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.6679em;"><span style="top:-2.3479em;margin-left:0em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.02778em;">θ</span></span></span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span><span class="mop">min</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.7521em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;"><span class="delimsizing size4">[</span></span><span class="mord">−</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.6514em;"><span style="top:-1.8723em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.05em;"><span class="pstrut" style="height:3.05em;"></span><span><span class="mop op-symbol large-op">∑</span></span></span><span style="top:-4.3em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">n</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.2777em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;"><span class="delimsizing size2">[</span></span><span class="mord"><span class="mord mathbf" style="margin-right:0.01597em;">y</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.938em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mathnormal mtight">i</span><span class="mclose mtight">)</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mop">ln</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">h</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.02778em;">θ</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord"><span class="mord mathbf">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.938em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mathnormal mtight">i</span><span class="mclose mtight">)</span></span></span></span></span></span></span></span></span><span class="mclose">))</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mopen">(</span><span class="mord">1</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord"><span class="mord mathbf" style="margin-right:0.01597em;">y</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.938em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mathnormal mtight">i</span><span class="mclose mtight">)</span></span></span></span></span></span></span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mop">ln</span><span class="mopen">(</span><span class="mord">1</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord"><span class="mord mathnormal">h</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.02778em;">θ</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord"><span class="mord mathbf">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.938em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mathnormal mtight">i</span><span class="mclose mtight">)</span></span></span></span></span></span></span></span></span><span class="mclose">))</span><span class="mclose delimcenter" style="top:0em;"><span class="delimsizing size2">]</span></span></span><span class="mclose delimcenter" style="top:0em;"><span class="delimsizing size4">]</span></span></span></span></span></span></span></p>
<p>可以看出，括号高度可以框住整个公式</p>
<p>因此在这种大型的公式中，使用大尺寸括号视觉效果更美观</p>
<h3 id="其他常见符号">其他常见符号</h3>
<table>
<thead>
<tr>
<th style="text-align:center">符号</th>
<th style="text-align:center">语法</th>
<th style="text-align:center">符号</th>
<th style="text-align:center">语法</th>
<th style="text-align:center">符号</th>
<th style="text-align:center">语法</th>
</tr>
</thead>
<tbody>
<tr>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">∀</mi></mrow><annotation encoding="application/x-tex">\forall</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord">∀</span></span></span></span></td>
<td style="text-align:center">\forall</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">∃</mi></mrow><annotation encoding="application/x-tex">\exist</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord">∃</span></span></span></span></td>
<td style="text-align:center">\exist</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">∠</mi></mrow><annotation encoding="application/x-tex">\angle</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6922em;"></span><span class="mord">∠</span></span></span></span></td>
<td style="text-align:center">\angle</td>
</tr>
<tr>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">∅</mi></mrow><annotation encoding="application/x-tex">\emptyset</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">∅</span></span></span></span></td>
<td style="text-align:center">\emptyset</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">∂</mi></mrow><annotation encoding="application/x-tex">\partial</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord" style="margin-right:0.05556em;">∂</span></span></span></span></td>
<td style="text-align:center">\partial</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">∞</mi></mrow><annotation encoding="application/x-tex">\infty</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord">∞</span></span></span></span></td>
<td style="text-align:center">\infty</td>
</tr>
<tr>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>…</mo></mrow><annotation encoding="application/x-tex">\ldots</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.123em;"></span><span class="minner">…</span></span></span></span></td>
<td style="text-align:center">\ldots</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>⋯</mo></mrow><annotation encoding="application/x-tex">\cdots</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.313em;"></span><span class="minner">⋯</span></span></span></span></td>
<td style="text-align:center">\cdots</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>…</mo></mrow><annotation encoding="application/x-tex">\dots</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.123em;"></span><span class="minner">…</span></span></span></span></td>
<td style="text-align:center">\dots</td>
</tr>
<tr>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi><mi mathvariant="normal">⋮</mi><mpadded height="0em" voffset="0em"><mspace mathbackground="black" width="0em" height="1.5em"></mspace></mpadded></mi></mrow><annotation encoding="application/x-tex">\vdots</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.53em;vertical-align:-0.03em;"></span><span class="mord"><span class="mord">⋮</span><span class="mord rule" style="border-right-width:0em;border-top-width:1.5em;bottom:0em;"></span></span></span></span></span></td>
<td style="text-align:center">\vdots</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>⋱</mo></mrow><annotation encoding="application/x-tex">\ddots</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.823em;"></span><span class="minner">⋱</span></span></span></span></td>
<td style="text-align:center">\ddots</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo mathvariant="normal">′</mo></mrow><annotation encoding="application/x-tex">\prime</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5556em;"></span><span class="mord">′</span></span></span></span></td>
<td style="text-align:center">\prime</td>
</tr>
<tr>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>∵</mo></mrow><annotation encoding="application/x-tex">\because</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6922em;"></span><span class="mrel amsrm">∵</span></span></span></span></td>
<td style="text-align:center">\because</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>∴</mo></mrow><annotation encoding="application/x-tex">\therefore</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6922em;"></span><span class="mrel amsrm">∴</span></span></span></span></td>
<td style="text-align:center">\therefore</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">□</mi></mrow><annotation encoding="application/x-tex">\Box</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.675em;"></span><span class="mord amsrm">□</span></span></span></span></td>
<td style="text-align:center">\Box</td>
</tr>
<tr>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">△</mi></mrow><annotation encoding="application/x-tex">\triangle</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord">△</span></span></span></span></td>
<td style="text-align:center">\triangle</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">§</mi></mrow><annotation encoding="application/x-tex">\S</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord">§</span></span></span></span></td>
<td style="text-align:center">\S</td>
<td style="text-align:center"></td>
<td style="text-align:center"></td>
</tr>
</tbody>
</table>
<h2 id="数学公式写法">数学公式写法</h2>
<h3 id="上下标">上下标</h3>
<ul>
<li><code>^</code>：上标+ <code>_</code>：下标</li>
</ul>
<p>例如:</p>
<ul>
<li><code>\sum_&#123;i=1&#125;^&#123;n&#125;X_n</code>表示<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></msubsup><msub><mi>X</mi><mi>n</mi></msub></mrow><annotation encoding="application/x-tex">\sum_{i=1}^{n}X_n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.104em;vertical-align:-0.2997em;"></span><span class="mop"><span class="mop op-symbol small-op" style="position:relative;top:0em;">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8043em;"><span style="top:-2.4003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.2029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">n</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2997em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.07847em;">X</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:-0.0785em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>+ <code>\int_&#123;0&#125;^&#123;\infty&#125;x^2dx</code>表示<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mo>∫</mo><mn>0</mn><mi mathvariant="normal">∞</mi></msubsup><msup><mi>x</mi><mn>2</mn></msup><mi>d</mi><mi>x</mi></mrow><annotation encoding="application/x-tex">\int_{0}^{\infty}x^2dx</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.2151em;vertical-align:-0.3558em;"></span><span class="mop"><span class="mop op-symbol small-op" style="margin-right:0.19445em;position:relative;top:-0.0006em;">∫</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8593em;"><span style="top:-2.3442em;margin-left:-0.1945em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">0</span></span></span></span><span style="top:-3.2579em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">∞</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.3558em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mord mathnormal">d</span><span class="mord mathnormal">x</span></span></span></span>+ <code>\prod_&#123;i=1&#125;^&#123;n&#125;X_n</code>表示<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mo>∏</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></msubsup><msub><mi>X</mi><mi>n</mi></msub></mrow><annotation encoding="application/x-tex">\prod_{i=1}^{n}X_n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.104em;vertical-align:-0.2997em;"></span><span class="mop"><span class="mop op-symbol small-op" style="position:relative;top:0em;">∏</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8043em;"><span style="top:-2.4003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.2029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">n</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2997em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.07847em;">X</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:-0.0785em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></li>
</ul>
<h3 id="分数">分数</h3>
<p>使用<code>\frac&#123;&#125;&#123;&#125;</code>即可，例如<code>\frac&#123;a&#125;&#123;b&#125;</code>表示<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><mi>a</mi><mi>b</mi></mfrac></mrow><annotation encoding="application/x-tex">\frac{a}{b}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.0404em;vertical-align:-0.345em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.6954em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">b</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">a</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></p>
<h3 id="插入文字">插入文字</h3>
<p>使用<code>\text</code>，例如<code>\text&#123;hello,world!&#125;</code>表示<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mtext>hello,world!</mtext></mrow><annotation encoding="application/x-tex">\text{hello,world!}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord text"><span class="mord">hello,world!</span></span></span></span></span></p>
<h3 id="常见函数">常见函数</h3>
<table>
<thead>
<tr>
<th style="text-align:center">函数</th>
<th style="text-align:center">语法</th>
<th style="text-align:center">函数</th>
<th style="text-align:center">语法</th>
<th style="text-align:center">函数</th>
<th style="text-align:center">语法</th>
</tr>
</thead>
<tbody>
<tr>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>log</mi><mo>⁡</mo><mo stretchy="false">(</mo><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">\log()</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mop">lo<span style="margin-right:0.01389em;">g</span></span><span class="mopen">(</span><span class="mclose">)</span></span></span></span></td>
<td style="text-align:center">\log()</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>ln</mi><mo>⁡</mo><mo stretchy="false">(</mo><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">\ln()</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mop">ln</span><span class="mopen">(</span><span class="mclose">)</span></span></span></span></td>
<td style="text-align:center">\ln()</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>lg</mi><mo>⁡</mo><mo stretchy="false">(</mo><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">\lg()</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mop">l<span style="margin-right:0.01389em;">g</span></span><span class="mopen">(</span><span class="mclose">)</span></span></span></span></td>
<td style="text-align:center">\lg()</td>
</tr>
<tr>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>max</mi><mo>⁡</mo></mrow><annotation encoding="application/x-tex">\max</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mop">max</span></span></span></span></td>
<td style="text-align:center">\max</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>min</mi><mo>⁡</mo></mrow><annotation encoding="application/x-tex">\min</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6679em;"></span><span class="mop">min</span></span></span></span></td>
<td style="text-align:center">\min</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mrow><mi>lim</mi><mo>⁡</mo></mrow><mrow><mi>x</mi><mo>→</mo><mi mathvariant="normal">∞</mi></mrow></msub></mrow><annotation encoding="application/x-tex">\lim_{x \to \infty}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8444em;vertical-align:-0.15em;"></span><span class="mop"><span class="mop">lim</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">x</span><span class="mrel mtight">→</span><span class="mord mtight">∞</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mrow><mi>lim</mi><mo>⁡</mo></mrow><mrow><mi>x</mi><mo>→</mo><mi mathvariant="normal">∞</mi></mrow></msub></mrow><annotation encoding="application/x-tex">\lim_{x \to \infty}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8444em;vertical-align:-0.15em;"></span><span class="mop"><span class="mop">lim</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">x</span><span class="mrel mtight">→</span><span class="mord mtight">∞</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></td>
</tr>
<tr>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>arg</mi><mo>⁡</mo><msub><mrow><mi>max</mi><mo>⁡</mo></mrow><mrow><mi>c</mi><mo>∈</mo><mi>C</mi></mrow></msub></mrow><annotation encoding="application/x-tex">\arg\max_{c \in C}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em;"></span><span class="mop">ar<span style="margin-right:0.01389em;">g</span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mop"><span class="mop">max</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">c</span><span class="mrel mtight">∈</span><span class="mord mathnormal mtight" style="margin-right:0.07153em;">C</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.1774em;"><span></span></span></span></span></span></span></span></span></span></td>
<td style="text-align:center">\arg\max_{c \in C}</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>arg</mi><mo>⁡</mo><msub><mrow><mi>min</mi><mo>⁡</mo></mrow><mrow><mi>c</mi><mo>∈</mo><mi>C</mi></mrow></msub></mrow><annotation encoding="application/x-tex">\arg\min_{c \in C}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8623em;vertical-align:-0.1944em;"></span><span class="mop">ar<span style="margin-right:0.01389em;">g</span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mop"><span class="mop">min</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">c</span><span class="mrel mtight">∈</span><span class="mord mathnormal mtight" style="margin-right:0.07153em;">C</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.1774em;"><span></span></span></span></span></span></span></span></span></span></td>
<td style="text-align:center">\arg\min_{c \in C}</td>
<td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>exp</mi><mo>⁡</mo></mrow><annotation encoding="application/x-tex">\exp</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em;"></span><span class="mop">exp</span></span></span></span></td>
<td style="text-align:center">\exp</td>
</tr>
</tbody>
</table>
<h3 id="矩阵、行列式">矩阵、行列式</h3>
<p><code>&amp;</code>表示分隔元素，<code>\\</code>表示换行</p>
<figure class="highlight dust"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br></pre></td><td class="code"><pre><span class="line"><span class="language-xml">A=</span></span><br><span class="line"><span class="language-xml">\begin</span><span class="template-variable">&#123;pmatrix&#125;</span><span class="language-xml"></span></span><br><span class="line"><span class="language-xml">a_</span><span class="template-variable">&#123;11&#125;</span><span class="language-xml"> &amp; a_</span><span class="template-variable">&#123;12&#125;</span><span class="language-xml"> \\</span></span><br><span class="line"><span class="language-xml">a_</span><span class="template-variable">&#123;21&#125;</span><span class="language-xml"> &amp; a_</span><span class="template-variable">&#123;22&#125;</span><span class="language-xml"></span></span><br><span class="line"><span class="language-xml">\end</span><span class="template-variable">&#123;pmatrix&#125;</span></span><br></pre></td></tr></table></figure>
<p><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>A</mi><mo>=</mo><mrow><mo fence="true">(</mo><mtable rowspacing="0.16em" columnalign="center center" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><msub><mi>a</mi><mn>11</mn></msub></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><msub><mi>a</mi><mn>12</mn></msub></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><msub><mi>a</mi><mn>21</mn></msub></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><msub><mi>a</mi><mn>22</mn></msub></mstyle></mtd></mtr></mtable><mo fence="true">)</mo></mrow></mrow><annotation encoding="application/x-tex">A= \begin{pmatrix} a_{11} &amp; a_{12} \\ a_{21} &amp; a_{22} \end{pmatrix}
</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal">A</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:2.4em;vertical-align:-0.95em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;"><span class="delimsizing size3">(</span></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.45em;"><span style="top:-3.61em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal">a</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">11</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span><span style="top:-2.41em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal">a</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">21</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.95em;"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em;"></span><span class="arraycolsep" style="width:0.5em;"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.45em;"><span style="top:-3.61em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal">a</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">12</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span><span style="top:-2.41em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal">a</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">22</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.95em;"><span></span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em;"><span class="delimsizing size3">)</span></span></span></span></span></span></span></p>
<figure class="highlight dust"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br></pre></td><td class="code"><pre><span class="line"><span class="language-xml">A=</span></span><br><span class="line"><span class="language-xml">\begin</span><span class="template-variable">&#123;bmatrix&#125;</span><span class="language-xml"></span></span><br><span class="line"><span class="language-xml">a_</span><span class="template-variable">&#123;11&#125;</span><span class="language-xml"> &amp; a_</span><span class="template-variable">&#123;12&#125;</span><span class="language-xml"> \\</span></span><br><span class="line"><span class="language-xml">a_</span><span class="template-variable">&#123;21&#125;</span><span class="language-xml"> &amp; a_</span><span class="template-variable">&#123;22&#125;</span><span class="language-xml"></span></span><br><span class="line"><span class="language-xml">\end</span><span class="template-variable">&#123;bmatrix&#125;</span></span><br></pre></td></tr></table></figure>
<p><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>A</mi><mo>=</mo><mrow><mo fence="true">[</mo><mtable rowspacing="0.16em" columnalign="center center" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><msub><mi>a</mi><mn>11</mn></msub></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><msub><mi>a</mi><mn>12</mn></msub></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><msub><mi>a</mi><mn>21</mn></msub></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><msub><mi>a</mi><mn>22</mn></msub></mstyle></mtd></mtr></mtable><mo fence="true">]</mo></mrow></mrow><annotation encoding="application/x-tex">A= \begin{bmatrix} a_{11} &amp; a_{12} \\ a_{21} &amp; a_{22} \end{bmatrix}
</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal">A</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:2.4em;vertical-align:-0.95em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;"><span class="delimsizing size3">[</span></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.45em;"><span style="top:-3.61em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal">a</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">11</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span><span style="top:-2.41em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal">a</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">21</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.95em;"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em;"></span><span class="arraycolsep" style="width:0.5em;"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.45em;"><span style="top:-3.61em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal">a</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">12</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span><span style="top:-2.41em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal">a</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">22</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.95em;"><span></span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em;"><span class="delimsizing size3">]</span></span></span></span></span></span></span></p>
<figure class="highlight dust"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br></pre></td><td class="code"><pre><span class="line"><span class="language-xml">A=</span></span><br><span class="line"><span class="language-xml">\begin</span><span class="template-variable">&#123;vmatrix&#125;</span><span class="language-xml"></span></span><br><span class="line"><span class="language-xml">a_</span><span class="template-variable">&#123;11&#125;</span><span class="language-xml"> &amp; a_</span><span class="template-variable">&#123;12&#125;</span><span class="language-xml"> \\</span></span><br><span class="line"><span class="language-xml">a_</span><span class="template-variable">&#123;21&#125;</span><span class="language-xml"> &amp; a_</span><span class="template-variable">&#123;22&#125;</span><span class="language-xml"></span></span><br><span class="line"><span class="language-xml">\end</span><span class="template-variable">&#123;vmatrix&#125;</span></span><br></pre></td></tr></table></figure>
<p><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>A</mi><mo>=</mo><mrow><mo fence="true">∣</mo><mtable rowspacing="0.16em" columnalign="center center" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><msub><mi>a</mi><mn>11</mn></msub></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><msub><mi>a</mi><mn>12</mn></msub></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><msub><mi>a</mi><mn>21</mn></msub></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><msub><mi>a</mi><mn>22</mn></msub></mstyle></mtd></mtr></mtable><mo fence="true">∣</mo></mrow></mrow><annotation encoding="application/x-tex">A= \begin{vmatrix} a_{11} &amp; a_{12} \\ a_{21} &amp; a_{22} \end{vmatrix}
</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal">A</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:2.4em;vertical-align:-0.95em;"></span><span class="minner"><span class="mopen"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.45em;"><span style="top:-3.45em;"><span class="pstrut" style="height:4.4em;"></span><span style="width:0.333em;height:2.400em;"><svg xmlns="http://www.w3.org/2000/svg" width='0.333em' height='2.400em' viewBox='0 0 333 2400'><path d='M145 15 v585 v1200 v585 c2.667,10,9.667,15,21,15
c10,0,16.667,-5,20,-15 v-585 v-1200 v-585 c-2.667,-10,-9.667,-15,-21,-15
c-10,0,-16.667,5,-20,15z M188 15 H145 v585 v1200 v585 h43z'/></svg></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.95em;"><span></span></span></span></span></span></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.45em;"><span style="top:-3.61em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal">a</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">11</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span><span style="top:-2.41em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal">a</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">21</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.95em;"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em;"></span><span class="arraycolsep" style="width:0.5em;"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.45em;"><span style="top:-3.61em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal">a</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">12</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span><span style="top:-2.41em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal">a</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">22</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.95em;"><span></span></span></span></span></span></span></span><span class="mclose"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.45em;"><span style="top:-3.45em;"><span class="pstrut" style="height:4.4em;"></span><span style="width:0.333em;height:2.400em;"><svg xmlns="http://www.w3.org/2000/svg" width='0.333em' height='2.400em' viewBox='0 0 333 2400'><path d='M145 15 v585 v1200 v585 c2.667,10,9.667,15,21,15
c10,0,16.667,-5,20,-15 v-585 v-1200 v-585 c-2.667,-10,-9.667,-15,-21,-15
c-10,0,-16.667,5,-20,15z M188 15 H145 v585 v1200 v585 h43z'/></svg></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.95em;"><span></span></span></span></span></span></span></span></span></span></span></span></p>
<h3 id="多行公式对齐">多行公式对齐</h3>
<p>使用<code>\begin&#123;split&#125; \end&#123;split&#125;</code>，在需要对齐的地方添加<code>&amp;</code>符号（默认为右对齐）</p>
<p>例如：</p>
<figure class="highlight dust"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br></pre></td><td class="code"><pre><span class="line"><span class="language-xml">\begin</span><span class="template-variable">&#123;split&#125;</span><span class="language-xml"></span></span><br><span class="line"><span class="language-xml">L(\theta)</span></span><br><span class="line"><span class="language-xml">&amp;=	\arg\max_</span><span class="template-variable">&#123;\theta&#125;</span><span class="language-xml">\ln(P_</span><span class="template-variable">&#123;All&#125;</span><span class="language-xml">)\\</span></span><br><span class="line"><span class="language-xml">&amp;=	\arg\max_</span><span class="template-variable">&#123;\theta&#125;</span><span class="language-xml">\ln\prod_</span><span class="template-variable">&#123;i=1&#125;</span><span class="language-xml">^</span><span class="template-variable">&#123;n&#125;</span><span class="language-xml"></span></span><br><span class="line"><span class="language-xml">    \left[</span></span><br><span class="line"><span class="language-xml">        (h_</span><span class="template-variable">&#123;\theta&#125;</span><span class="language-xml">(\mathbf</span><span class="template-variable">&#123;x&#125;</span><span class="language-xml">^</span><span class="template-variable">&#123;(i)&#125;</span><span class="language-xml">))^</span><span class="template-variable">&#123;\mathbf&#123;y&#125;</span><span class="language-xml">^</span><span class="template-variable">&#123;(i)&#125;</span><span class="language-xml">&#125;\cdot</span></span><br><span class="line"><span class="language-xml">        (1-h_</span><span class="template-variable">&#123;\theta&#125;</span><span class="language-xml">(\mathbf</span><span class="template-variable">&#123;x&#125;</span><span class="language-xml">^</span><span class="template-variable">&#123;(i)&#125;</span><span class="language-xml">))^</span><span class="template-variable">&#123;1-\mathbf&#123;y&#125;</span><span class="language-xml">^</span><span class="template-variable">&#123;(i)&#125;</span><span class="language-xml">&#125;</span></span><br><span class="line"><span class="language-xml">    \right]\\</span></span><br><span class="line"><span class="language-xml">&amp;=	\arg\max_</span><span class="template-variable">&#123;\theta&#125;</span><span class="language-xml">\sum_</span><span class="template-variable">&#123;i=1&#125;</span><span class="language-xml">^</span><span class="template-variable">&#123;n&#125;</span><span class="language-xml"></span></span><br><span class="line"><span class="language-xml">	\left[</span></span><br><span class="line"><span class="language-xml">		\mathbf</span><span class="template-variable">&#123;y&#125;</span><span class="language-xml">^</span><span class="template-variable">&#123;(i)&#125;</span><span class="language-xml">\ln(h_</span><span class="template-variable">&#123;\theta&#125;</span><span class="language-xml">(\mathbf</span><span class="template-variable">&#123;x&#125;</span><span class="language-xml">^</span><span class="template-variable">&#123;(i)&#125;</span><span class="language-xml">)) +</span></span><br><span class="line"><span class="language-xml">		(1-\mathbf</span><span class="template-variable">&#123;y&#125;</span><span class="language-xml">^</span><span class="template-variable">&#123;(i)&#125;</span><span class="language-xml">)\ln(1-h_</span><span class="template-variable">&#123;\theta&#125;</span><span class="language-xml">(\mathbf</span><span class="template-variable">&#123;x&#125;</span><span class="language-xml">^</span><span class="template-variable">&#123;(i)&#125;</span><span class="language-xml">))</span></span><br><span class="line"><span class="language-xml">	\right]\\</span></span><br><span class="line"><span class="language-xml">&amp;=	\arg\min_</span><span class="template-variable">&#123;\theta&#125;</span><span class="language-xml"></span></span><br><span class="line"><span class="language-xml">	\left[</span></span><br><span class="line"><span class="language-xml">        -\sum_</span><span class="template-variable">&#123;i=1&#125;</span><span class="language-xml">^</span><span class="template-variable">&#123;n&#125;</span><span class="language-xml"></span></span><br><span class="line"><span class="language-xml">        \left[</span></span><br><span class="line"><span class="language-xml">            \mathbf</span><span class="template-variable">&#123;y&#125;</span><span class="language-xml">^</span><span class="template-variable">&#123;(i)&#125;</span><span class="language-xml">\ln(h_</span><span class="template-variable">&#123;\theta&#125;</span><span class="language-xml">(\mathbf</span><span class="template-variable">&#123;x&#125;</span><span class="language-xml">^</span><span class="template-variable">&#123;(i)&#125;</span><span class="language-xml">)) +</span></span><br><span class="line"><span class="language-xml">            (1-\mathbf</span><span class="template-variable">&#123;y&#125;</span><span class="language-xml">^</span><span class="template-variable">&#123;(i)&#125;</span><span class="language-xml">)\ln(1-h_</span><span class="template-variable">&#123;\theta&#125;</span><span class="language-xml">(\mathbf</span><span class="template-variable">&#123;x&#125;</span><span class="language-xml">^</span><span class="template-variable">&#123;(i)&#125;</span><span class="language-xml">))</span></span><br><span class="line"><span class="language-xml">        \right]</span></span><br><span class="line"><span class="language-xml">	\right]\\</span></span><br><span class="line"><span class="language-xml">&amp;=	\arg\min_</span><span class="template-variable">&#123;\theta&#125;</span><span class="language-xml">\mathscr</span><span class="template-variable">&#123;l&#125;</span><span class="language-xml">(\theta)</span></span><br><span class="line"><span class="language-xml">\end</span><span class="template-variable">&#123;split&#125;</span></span><br></pre></td></tr></table></figure>
<p><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mtable rowspacing="0.25em" columnalign="right left" columnspacing="0em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mi>L</mi><mo stretchy="false">(</mo><mi>θ</mi><mo stretchy="false">)</mo></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mi>arg</mi><mo>⁡</mo><munder><mrow><mi>max</mi><mo>⁡</mo></mrow><mi>θ</mi></munder><mi>ln</mi><mo>⁡</mo><mo stretchy="false">(</mo><msub><mi>P</mi><mrow><mi>A</mi><mi>l</mi><mi>l</mi></mrow></msub><mo stretchy="false">)</mo></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mi>arg</mi><mo>⁡</mo><munder><mrow><mi>max</mi><mo>⁡</mo></mrow><mi>θ</mi></munder><mi>ln</mi><mo>⁡</mo><munderover><mo>∏</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></munderover><mrow><mo fence="true">[</mo><mo stretchy="false">(</mo><msub><mi>h</mi><mi>θ</mi></msub><mo stretchy="false">(</mo><msup><mi mathvariant="bold">x</mi><mrow><mo stretchy="false">(</mo><mi>i</mi><mo stretchy="false">)</mo></mrow></msup><mo stretchy="false">)</mo><msup><mo stretchy="false">)</mo><msup><mi mathvariant="bold">y</mi><mrow><mo stretchy="false">(</mo><mi>i</mi><mo stretchy="false">)</mo></mrow></msup></msup><mo>⋅</mo><mo stretchy="false">(</mo><mn>1</mn><mo>−</mo><msub><mi>h</mi><mi>θ</mi></msub><mo stretchy="false">(</mo><msup><mi mathvariant="bold">x</mi><mrow><mo stretchy="false">(</mo><mi>i</mi><mo stretchy="false">)</mo></mrow></msup><mo stretchy="false">)</mo><msup><mo stretchy="false">)</mo><mrow><mn>1</mn><mo>−</mo><msup><mi mathvariant="bold">y</mi><mrow><mo stretchy="false">(</mo><mi>i</mi><mo stretchy="false">)</mo></mrow></msup></mrow></msup><mo fence="true">]</mo></mrow></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mi>arg</mi><mo>⁡</mo><munder><mrow><mi>max</mi><mo>⁡</mo></mrow><mi>θ</mi></munder><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></munderover><mrow><mo fence="true">[</mo><msup><mi mathvariant="bold">y</mi><mrow><mo stretchy="false">(</mo><mi>i</mi><mo stretchy="false">)</mo></mrow></msup><mi>ln</mi><mo>⁡</mo><mo stretchy="false">(</mo><msub><mi>h</mi><mi>θ</mi></msub><mo stretchy="false">(</mo><msup><mi mathvariant="bold">x</mi><mrow><mo stretchy="false">(</mo><mi>i</mi><mo stretchy="false">)</mo></mrow></msup><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo>+</mo><mo stretchy="false">(</mo><mn>1</mn><mo>−</mo><msup><mi mathvariant="bold">y</mi><mrow><mo stretchy="false">(</mo><mi>i</mi><mo stretchy="false">)</mo></mrow></msup><mo stretchy="false">)</mo><mi>ln</mi><mo>⁡</mo><mo stretchy="false">(</mo><mn>1</mn><mo>−</mo><msub><mi>h</mi><mi>θ</mi></msub><mo stretchy="false">(</mo><msup><mi mathvariant="bold">x</mi><mrow><mo stretchy="false">(</mo><mi>i</mi><mo stretchy="false">)</mo></mrow></msup><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo fence="true">]</mo></mrow></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mi>arg</mi><mo>⁡</mo><munder><mrow><mi>min</mi><mo>⁡</mo></mrow><mi>θ</mi></munder><mrow><mo fence="true">[</mo><mo>−</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></munderover><mrow><mo fence="true">[</mo><msup><mi mathvariant="bold">y</mi><mrow><mo stretchy="false">(</mo><mi>i</mi><mo stretchy="false">)</mo></mrow></msup><mi>ln</mi><mo>⁡</mo><mo stretchy="false">(</mo><msub><mi>h</mi><mi>θ</mi></msub><mo stretchy="false">(</mo><msup><mi mathvariant="bold">x</mi><mrow><mo stretchy="false">(</mo><mi>i</mi><mo stretchy="false">)</mo></mrow></msup><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo>+</mo><mo stretchy="false">(</mo><mn>1</mn><mo>−</mo><msup><mi mathvariant="bold">y</mi><mrow><mo stretchy="false">(</mo><mi>i</mi><mo stretchy="false">)</mo></mrow></msup><mo stretchy="false">)</mo><mi>ln</mi><mo>⁡</mo><mo stretchy="false">(</mo><mn>1</mn><mo>−</mo><msub><mi>h</mi><mi>θ</mi></msub><mo stretchy="false">(</mo><msup><mi mathvariant="bold">x</mi><mrow><mo stretchy="false">(</mo><mi>i</mi><mo stretchy="false">)</mo></mrow></msup><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo fence="true">]</mo></mrow><mo fence="true">]</mo></mrow></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mi>arg</mi><mo>⁡</mo><munder><mrow><mi>min</mi><mo>⁡</mo></mrow><mi>θ</mi></munder><mi mathvariant="script">l</mi><mo stretchy="false">(</mo><mi>θ</mi><mo stretchy="false">)</mo></mrow></mstyle></mtd></mtr></mtable><annotation encoding="application/x-tex">\begin{split} L(\theta) &amp;= \arg\max_{\theta}\ln(P_{All})\\ &amp;= \arg\max_{\theta}\ln\prod_{i=1}^{n} \left[ (h_{\theta}(\mathbf{x}^{(i)}))^{\mathbf{y}^{(i)}}\cdot (1-h_{\theta}(\mathbf{x}^{(i)}))^{1-\mathbf{y}^{(i)}} \right]\\ &amp;= \arg\max_{\theta}\sum_{i=1}^{n} \left[ \mathbf{y}^{(i)}\ln(h_{\theta}(\mathbf{x}^{(i)})) + (1-\mathbf{y}^{(i)})\ln(1-h_{\theta}(\mathbf{x}^{(i)})) \right]\\ &amp;= \arg\min_{\theta} \left[ -\sum_{i=1}^{n} \left[ \mathbf{y}^{(i)}\ln(h_{\theta}(\mathbf{x}^{(i)})) + (1-\mathbf{y}^{(i)})\ln(1-h_{\theta}(\mathbf{x}^{(i)})) \right] \right]\\ &amp;= \arg\min_{\theta}\mathscr{l}(\theta) \end{split}
</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:13.57em;vertical-align:-6.535em;"></span><span class="mord"><span class="mtable"><span class="col-align-r"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:7.035em;"><span style="top:-9.945em;"><span class="pstrut" style="height:3.75em;"></span><span class="mord"><span class="mord mathnormal">L</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.02778em;">θ</span><span class="mclose">)</span></span></span><span style="top:-7.2415em;"><span class="pstrut" style="height:3.75em;"></span><span class="mord"></span></span><span style="top:-4.0124em;"><span class="pstrut" style="height:3.75em;"></span><span class="mord"></span></span><span style="top:-0.6848em;"><span class="pstrut" style="height:3.75em;"></span><span class="mord"></span></span><span style="top:1.7329em;"><span class="pstrut" style="height:3.75em;"></span><span class="mord"></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:6.535em;"><span></span></span></span></span></span><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:7.035em;"><span style="top:-9.945em;"><span class="pstrut" style="height:3.75em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mop">ar<span style="margin-right:0.01389em;">g</span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.4306em;"><span style="top:-2.3479em;margin-left:0em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.02778em;">θ</span></span></span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span><span class="mop">max</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.7521em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mop">ln</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">A</span><span class="mord mathnormal mtight" style="margin-right:0.01968em;">ll</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span></span></span><span style="top:-7.2415em;"><span class="pstrut" style="height:3.75em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mop">ar<span style="margin-right:0.01389em;">g</span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.4306em;"><span style="top:-2.3479em;margin-left:0em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.02778em;">θ</span></span></span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span><span class="mop">max</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.7521em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mop">ln</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.6514em;"><span style="top:-1.8723em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.05em;"><span class="pstrut" style="height:3.05em;"></span><span><span class="mop op-symbol large-op">∏</span></span></span><span style="top:-4.3em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">n</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.2777em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;"><span class="delimsizing size2">[</span></span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">h</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.02778em;">θ</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord"><span class="mord mathbf">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.938em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mathnormal mtight">i</span><span class="mclose mtight">)</span></span></span></span></span></span></span></span></span><span class="mclose">)</span><span class="mclose"><span class="mclose">)</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:1.0897em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathbf mtight" style="margin-right:0.01597em;">y</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9667em;"><span style="top:-2.9667em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5357em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mathnormal mtight">i</span><span class="mclose mtight">)</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mopen">(</span><span class="mord">1</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord"><span class="mord mathnormal">h</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.02778em;">θ</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord"><span class="mord mathbf">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.938em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mathnormal mtight">i</span><span class="mclose mtight">)</span></span></span></span></span></span></span></span></span><span class="mclose">)</span><span class="mclose"><span class="mclose">)</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:1.0897em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1</span><span class="mbin mtight">−</span><span class="mord mtight"><span class="mord mathbf mtight" style="margin-right:0.01597em;">y</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9667em;"><span style="top:-2.9667em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5357em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mathnormal mtight">i</span><span class="mclose mtight">)</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em;"><span class="delimsizing size2">]</span></span></span></span></span><span style="top:-4.0124em;"><span class="pstrut" style="height:3.75em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mop">ar<span style="margin-right:0.01389em;">g</span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.4306em;"><span style="top:-2.3479em;margin-left:0em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.02778em;">θ</span></span></span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span><span class="mop">max</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.7521em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.6514em;"><span style="top:-1.8723em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.05em;"><span class="pstrut" style="height:3.05em;"></span><span><span class="mop op-symbol large-op">∑</span></span></span><span style="top:-4.3em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">n</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.2777em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;"><span class="delimsizing size2">[</span></span><span class="mord"><span class="mord mathbf" style="margin-right:0.01597em;">y</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.938em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mathnormal mtight">i</span><span class="mclose mtight">)</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mop">ln</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">h</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.02778em;">θ</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord"><span class="mord mathbf">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.938em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mathnormal mtight">i</span><span class="mclose mtight">)</span></span></span></span></span></span></span></span></span><span class="mclose">))</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mopen">(</span><span class="mord">1</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord"><span class="mord mathbf" style="margin-right:0.01597em;">y</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.938em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mathnormal mtight">i</span><span class="mclose mtight">)</span></span></span></span></span></span></span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mop">ln</span><span class="mopen">(</span><span class="mord">1</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord"><span class="mord mathnormal">h</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.02778em;">θ</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord"><span class="mord mathbf">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.938em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mathnormal mtight">i</span><span class="mclose mtight">)</span></span></span></span></span></span></span></span></span><span class="mclose">))</span><span class="mclose delimcenter" style="top:0em;"><span class="delimsizing size2">]</span></span></span></span></span><span style="top:-0.6848em;"><span class="pstrut" style="height:3.75em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mop">ar<span style="margin-right:0.01389em;">g</span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.6679em;"><span style="top:-2.3479em;margin-left:0em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.02778em;">θ</span></span></span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span><span class="mop">min</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.7521em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;"><span class="delimsizing size4">[</span></span><span class="mord">−</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.6514em;"><span style="top:-1.8723em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.05em;"><span class="pstrut" style="height:3.05em;"></span><span><span class="mop op-symbol large-op">∑</span></span></span><span style="top:-4.3em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">n</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.2777em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;"><span class="delimsizing size2">[</span></span><span class="mord"><span class="mord mathbf" style="margin-right:0.01597em;">y</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.938em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mathnormal mtight">i</span><span class="mclose mtight">)</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mop">ln</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">h</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.02778em;">θ</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord"><span class="mord mathbf">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.938em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mathnormal mtight">i</span><span class="mclose mtight">)</span></span></span></span></span></span></span></span></span><span class="mclose">))</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mopen">(</span><span class="mord">1</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord"><span class="mord mathbf" style="margin-right:0.01597em;">y</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.938em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mathnormal mtight">i</span><span class="mclose mtight">)</span></span></span></span></span></span></span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mop">ln</span><span class="mopen">(</span><span class="mord">1</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord"><span class="mord mathnormal">h</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.02778em;">θ</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord"><span class="mord mathbf">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.938em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mathnormal mtight">i</span><span class="mclose mtight">)</span></span></span></span></span></span></span></span></span><span class="mclose">))</span><span class="mclose delimcenter" style="top:0em;"><span class="delimsizing size2">]</span></span></span><span class="mclose delimcenter" style="top:0em;"><span class="delimsizing size4">]</span></span></span></span></span><span style="top:1.7329em;"><span class="pstrut" style="height:3.75em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mop">ar<span style="margin-right:0.01389em;">g</span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.6679em;"><span style="top:-2.3479em;margin-left:0em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.02778em;">θ</span></span></span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span><span class="mop">min</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.7521em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.02778em;">θ</span><span class="mclose">)</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:6.535em;"><span></span></span></span></span></span></span></span></span></span></span></span></p>
<p>上例中，在<code>=</code>前添加了<code>&amp;</code>，因此实现<strong>等号对齐</strong></p>
<p>如果希望<strong>左对齐</strong>，例如</p>
<figure class="highlight excel"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br></pre></td><td class="code"><pre><span class="line">\begin&#123;split&#125;</span><br><span class="line">&amp;\l<span class="built_in">n</span> h_&#123;\theta&#125;(\mathbf&#123;x&#125;^&#123;(i)&#125;)</span><br><span class="line">=	\l<span class="built_in">n</span>\frac&#123;<span class="number">1</span>&#125;&#123;<span class="number">1</span>+e^&#123;-\theta^<span class="built_in">T</span> \mathbf&#123;x&#125;^&#123;(i)&#125;&#125;&#125;</span><br><span class="line">= 	-\l<span class="built_in">n</span>(<span class="number">1</span>+e^&#123;\theta^<span class="built_in">T</span> \mathbf&#123;x&#125;^&#123;(i)&#125;&#125;)\\</span><br><span class="line">&amp;\l<span class="built_in">n</span>(<span class="number">1</span>-h_&#123;\theta&#125;(\mathbf&#123;x&#125;^&#123;(i)&#125;))</span><br><span class="line">=	\l<span class="built_in">n</span>(<span class="number">1</span>-\frac&#123;<span class="number">1</span>&#125;&#123;<span class="number">1</span>+e^&#123;-\theta^<span class="built_in">T</span> \mathbf&#123;x&#125;^&#123;(i)&#125;&#125;&#125;)</span><br><span class="line">= 	-\theta^<span class="built_in">T</span> \mathbf&#123;x&#125;^&#123;(i)&#125;-\l<span class="built_in">n</span>(<span class="number">1</span>+e^&#123;\theta^<span class="built_in">T</span> \mathbf&#123;x&#125;^&#123;(i)&#125;&#125;)</span><br><span class="line">\end&#123;split&#125;</span><br></pre></td></tr></table></figure>
<p><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mtable rowspacing="0.25em" columnalign="right left" columnspacing="0em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mi>ln</mi><mo>⁡</mo><msub><mi>h</mi><mi>θ</mi></msub><mo stretchy="false">(</mo><msup><mi mathvariant="bold">x</mi><mrow><mo stretchy="false">(</mo><mi>i</mi><mo stretchy="false">)</mo></mrow></msup><mo stretchy="false">)</mo><mo>=</mo><mi>ln</mi><mo>⁡</mo><mfrac><mn>1</mn><mrow><mn>1</mn><mo>+</mo><msup><mi>e</mi><mrow><mo>−</mo><msup><mi>θ</mi><mi>T</mi></msup><msup><mi mathvariant="bold">x</mi><mrow><mo stretchy="false">(</mo><mi>i</mi><mo stretchy="false">)</mo></mrow></msup></mrow></msup></mrow></mfrac><mo>=</mo><mo>−</mo><mi>ln</mi><mo>⁡</mo><mo stretchy="false">(</mo><mn>1</mn><mo>+</mo><msup><mi>e</mi><mrow><msup><mi>θ</mi><mi>T</mi></msup><msup><mi mathvariant="bold">x</mi><mrow><mo stretchy="false">(</mo><mi>i</mi><mo stretchy="false">)</mo></mrow></msup></mrow></msup><mo stretchy="false">)</mo></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mi>ln</mi><mo>⁡</mo><mo stretchy="false">(</mo><mn>1</mn><mo>−</mo><msub><mi>h</mi><mi>θ</mi></msub><mo stretchy="false">(</mo><msup><mi mathvariant="bold">x</mi><mrow><mo stretchy="false">(</mo><mi>i</mi><mo stretchy="false">)</mo></mrow></msup><mo stretchy="false">)</mo><mo stretchy="false">)</mo><mo>=</mo><mi>ln</mi><mo>⁡</mo><mo stretchy="false">(</mo><mn>1</mn><mo>−</mo><mfrac><mn>1</mn><mrow><mn>1</mn><mo>+</mo><msup><mi>e</mi><mrow><mo>−</mo><msup><mi>θ</mi><mi>T</mi></msup><msup><mi mathvariant="bold">x</mi><mrow><mo stretchy="false">(</mo><mi>i</mi><mo stretchy="false">)</mo></mrow></msup></mrow></msup></mrow></mfrac><mo stretchy="false">)</mo><mo>=</mo><mo>−</mo><msup><mi>θ</mi><mi>T</mi></msup><msup><mi mathvariant="bold">x</mi><mrow><mo stretchy="false">(</mo><mi>i</mi><mo stretchy="false">)</mo></mrow></msup><mo>−</mo><mi>ln</mi><mo>⁡</mo><mo stretchy="false">(</mo><mn>1</mn><mo>+</mo><msup><mi>e</mi><mrow><msup><mi>θ</mi><mi>T</mi></msup><msup><mi mathvariant="bold">x</mi><mrow><mo stretchy="false">(</mo><mi>i</mi><mo stretchy="false">)</mo></mrow></msup></mrow></msup><mo stretchy="false">)</mo></mrow></mstyle></mtd></mtr></mtable><annotation encoding="application/x-tex">\begin{split} &amp;\ln h_{\theta}(\mathbf{x}^{(i)}) = \ln\frac{1}{1+e^{-\theta^T \mathbf{x}^{(i)}}} = -\ln(1+e^{\theta^T \mathbf{x}^{(i)}})\\ &amp;\ln(1-h_{\theta}(\mathbf{x}^{(i)})) = \ln(1-\frac{1}{1+e^{-\theta^T \mathbf{x}^{(i)}}}) = -\theta^T \mathbf{x}^{(i)}-\ln(1+e^{\theta^T \mathbf{x}^{(i)}}) \end{split}
</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:4.9184em;vertical-align:-2.2092em;"></span><span class="mord"><span class="mtable"><span class="col-align-r"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.7092em;"><span style="top:-4.7092em;"><span class="pstrut" style="height:3.3214em;"></span><span class="mord"></span></span><span style="top:-2.25em;"><span class="pstrut" style="height:3.3214em;"></span><span class="mord"></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:2.2092em;"><span></span></span></span></span></span><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.7092em;"><span style="top:-4.7092em;"><span class="pstrut" style="height:3.3214em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mop">ln</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal">h</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.02778em;">θ</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord"><span class="mord mathbf">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.938em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mathnormal mtight">i</span><span class="mclose mtight">)</span></span></span></span></span></span></span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mop">ln</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3214em;"><span style="top:-2.2456em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord"><span class="mord mathnormal">e</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8644em;"><span style="top:-2.989em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">−</span><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.02778em;">θ</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7741em;"><span style="top:-2.786em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mathnormal mtight" style="margin-right:0.13889em;">T</span></span></span></span></span></span></span></span><span class="mord mtight"><span class="mord mathbf mtight">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.822em;"><span style="top:-2.822em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5357em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mathnormal mtight">i</span><span class="mclose mtight">)</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.8378em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">−</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mop">ln</span><span class="mopen">(</span><span class="mord">1</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord"><span class="mord mathnormal">e</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:1.0897em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.02778em;">θ</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9191em;"><span style="top:-2.931em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mathnormal mtight" style="margin-right:0.13889em;">T</span></span></span></span></span></span></span></span><span class="mord mtight"><span class="mord mathbf mtight">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9667em;"><span style="top:-2.9667em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5357em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mathnormal mtight">i</span><span class="mclose mtight">)</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span class="mclose">)</span></span></span><span style="top:-2.25em;"><span class="pstrut" style="height:3.3214em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mop">ln</span><span class="mopen">(</span><span class="mord">1</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord"><span class="mord mathnormal">h</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.02778em;">θ</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord"><span class="mord mathbf">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.938em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mathnormal mtight">i</span><span class="mclose mtight">)</span></span></span></span></span></span></span></span></span><span class="mclose">))</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mop">ln</span><span class="mopen">(</span><span class="mord">1</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3214em;"><span style="top:-2.2456em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord"><span class="mord mathnormal">e</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8644em;"><span style="top:-2.989em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">−</span><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.02778em;">θ</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7741em;"><span style="top:-2.786em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mathnormal mtight" style="margin-right:0.13889em;">T</span></span></span></span></span></span></span></span><span class="mord mtight"><span class="mord mathbf mtight">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.822em;"><span style="top:-2.822em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5357em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mathnormal mtight">i</span><span class="mclose mtight">)</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.8378em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">−</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.02778em;">θ</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8913em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.13889em;">T</span></span></span></span></span></span></span></span><span class="mord"><span class="mord mathbf">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.938em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mathnormal mtight">i</span><span class="mclose mtight">)</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mop">ln</span><span class="mopen">(</span><span class="mord">1</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord"><span class="mord mathnormal">e</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:1.0897em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.02778em;">θ</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9191em;"><span style="top:-2.931em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mathnormal mtight" style="margin-right:0.13889em;">T</span></span></span></span></span></span></span></span><span class="mord mtight"><span class="mord mathbf mtight">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9667em;"><span style="top:-2.9667em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5357em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mathnormal mtight">i</span><span class="mclose mtight">)</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:2.2092em;"><span></span></span></span></span></span></span></span></span></span></span></span></p>
<h3 id="方程组">方程组</h3>
<p>使用<code>\begin&#123;cases&#125; \end&#123;cases&#125;</code></p>
<p>例如：</p>
<figure class="highlight dust"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br></pre></td><td class="code"><pre><span class="line"><span class="language-xml">\begin</span><span class="template-variable">&#123;cases&#125;</span><span class="language-xml"></span></span><br><span class="line"><span class="language-xml">    \begin</span><span class="template-variable">&#123;split&#125;</span><span class="language-xml"></span></span><br><span class="line"><span class="language-xml">        p &amp;= P(y=1|\mathbf</span><span class="template-variable">&#123;x&#125;</span><span class="language-xml">)=</span></span><br><span class="line"><span class="language-xml">        	\frac</span><span class="template-variable">&#123;1&#125;</span><span class="template-variable">&#123;1+e^&#123;-\theta^T\mathbf&#123;X&#125;</span><span class="language-xml">&#125;&#125;\\</span></span><br><span class="line"><span class="language-xml">        1-p &amp;= P(y=0|\mathbf</span><span class="template-variable">&#123;x&#125;</span><span class="language-xml">)=1-P(y=1|\mathbf</span><span class="template-variable">&#123;x&#125;</span><span class="language-xml">)=</span></span><br><span class="line"><span class="language-xml">        	\frac</span><span class="template-variable">&#123;1&#125;</span><span class="template-variable">&#123;1+e^&#123;\theta^T\mathbf&#123;X&#125;</span><span class="language-xml">&#125;&#125;</span></span><br><span class="line"><span class="language-xml">    \end</span><span class="template-variable">&#123;split&#125;</span><span class="language-xml"></span></span><br><span class="line"><span class="language-xml">\end</span><span class="template-variable">&#123;cases&#125;</span></span><br></pre></td></tr></table></figure>
<p><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mo fence="true">{</mo><mtable rowspacing="0.36em" columnalign="left left" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mtable rowspacing="0.25em" columnalign="right left" columnspacing="0em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mi>p</mi></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mi>P</mi><mo stretchy="false">(</mo><mi>y</mi><mo>=</mo><mn>1</mn><mi mathvariant="normal">∣</mi><mi mathvariant="bold">x</mi><mo stretchy="false">)</mo><mo>=</mo><mfrac><mn>1</mn><mrow><mn>1</mn><mo>+</mo><msup><mi>e</mi><mrow><mo>−</mo><msup><mi>θ</mi><mi>T</mi></msup><mi mathvariant="bold">X</mi></mrow></msup></mrow></mfrac></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mn>1</mn><mo>−</mo><mi>p</mi></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mi>P</mi><mo stretchy="false">(</mo><mi>y</mi><mo>=</mo><mn>0</mn><mi mathvariant="normal">∣</mi><mi mathvariant="bold">x</mi><mo stretchy="false">)</mo><mo>=</mo><mn>1</mn><mo>−</mo><mi>P</mi><mo stretchy="false">(</mo><mi>y</mi><mo>=</mo><mn>1</mn><mi mathvariant="normal">∣</mi><mi mathvariant="bold">x</mi><mo stretchy="false">)</mo><mo>=</mo><mfrac><mn>1</mn><mrow><mn>1</mn><mo>+</mo><msup><mi>e</mi><mrow><msup><mi>θ</mi><mi>T</mi></msup><mi mathvariant="bold">X</mi></mrow></msup></mrow></mfrac></mrow></mstyle></mtd></mtr></mtable></mstyle></mtd></mtr></mtable></mrow><annotation encoding="application/x-tex">\begin{cases} \begin{split} p &amp;= P(y=1|\mathbf{x})= \frac{1}{1+e^{-\theta^T\mathbf{X}}}\\ 1-p &amp;= P(y=0|\mathbf{x})=1-P(y=1|\mathbf{x})= \frac{1}{1+e^{\theta^T\mathbf{X}}} \end{split} \end{cases}
</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:4.8513em;vertical-align:-2.1756em;"></span><span class="minner"><span class="mopen"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.65em;"><span style="top:-1.9em;"><span class="pstrut" style="height:3.15em;"></span><span class="delimsizinginner delim-size4"><span>⎩</span></span></span><span style="top:-1.892em;"><span class="pstrut" style="height:3.15em;"></span><span style="height:0.616em;width:0.8889em;"><svg xmlns="http://www.w3.org/2000/svg" width='0.8889em' height='0.616em' style='width:0.8889em' viewBox='0 0 888.89 616' preserveAspectRatio='xMinYMin'><path d='M384 0 H504 V616 H384z M384 0 H504 V616 H384z'/></svg></span></span><span style="top:-3.15em;"><span class="pstrut" style="height:3.15em;"></span><span class="delimsizinginner delim-size4"><span>⎨</span></span></span><span style="top:-4.292em;"><span class="pstrut" style="height:3.15em;"></span><span style="height:0.616em;width:0.8889em;"><svg xmlns="http://www.w3.org/2000/svg" width='0.8889em' height='0.616em' style='width:0.8889em' viewBox='0 0 888.89 616' preserveAspectRatio='xMinYMin'><path d='M384 0 H504 V616 H384z M384 0 H504 V616 H384z'/></svg></span></span><span style="top:-4.9em;"><span class="pstrut" style="height:3.15em;"></span><span class="delimsizinginner delim-size4"><span>⎧</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:2.15em;"><span></span></span></span></span></span></span><span class="mord"><span class="mtable"><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.6756em;"><span style="top:-4.6756em;"><span class="pstrut" style="height:4.6756em;"></span><span class="mord"><span class="mord"><span class="mtable"><span class="col-align-r"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.6756em;"><span style="top:-4.6756em;"><span class="pstrut" style="height:3.3214em;"></span><span class="mord"><span class="mord mathnormal">p</span></span></span><span style="top:-2.25em;"><span class="pstrut" style="height:3.3214em;"></span><span class="mord"><span class="mord">1</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord mathnormal">p</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:2.1756em;"><span></span></span></span></span></span><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.6756em;"><span style="top:-4.6756em;"><span class="pstrut" style="height:3.3214em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">1∣</span><span class="mord mathbf">x</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3214em;"><span style="top:-2.2791em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord"><span class="mord mathnormal">e</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8309em;"><span style="top:-2.989em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">−</span><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.02778em;">θ</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7741em;"><span style="top:-2.786em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mathnormal mtight" style="margin-right:0.13889em;">T</span></span></span></span></span></span></span></span><span class="mord mathbf mtight">X</span></span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.8042em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span><span style="top:-2.25em;"><span class="pstrut" style="height:3.3214em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">0∣</span><span class="mord mathbf">x</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">1∣</span><span class="mord mathbf">x</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3214em;"><span style="top:-2.2791em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord"><span class="mord mathnormal">e</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8309em;"><span style="top:-2.989em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.02778em;">θ</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7741em;"><span style="top:-2.786em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mathnormal mtight" style="margin-right:0.13889em;">T</span></span></span></span></span></span></span></span><span class="mord mathbf mtight">X</span></span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.8042em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:2.1756em;"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:2.1756em;"><span></span></span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></p>
<figure class="highlight livescript"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br></pre></td><td class="code"><pre><span class="line"><span class="string">\text&#123;Decision</span> Boundary&#125;=</span><br><span class="line"><span class="string">\begin&#123;cases&#125;</span></span><br><span class="line">    <span class="number">1</span><span class="string">\quad</span> <span class="string">\text&#123;if</span> &#125;<span class="string">\</span> <span class="string">\hat&#123;y&#125;&gt;0.5\\</span></span><br><span class="line">    <span class="number">0</span><span class="string">\quad</span> <span class="string">\text&#123;otherwise&#125;</span></span><br><span class="line"><span class="string">\end&#123;cases&#125;</span></span><br></pre></td></tr></table></figure>
<p><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mtext>Decision Boundary</mtext><mo>=</mo><mrow><mo fence="true">{</mo><mtable rowspacing="0.36em" columnalign="left left" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mn>1</mn><mspace width="1em"/><mtext>if  </mtext><mover accent="true"><mi>y</mi><mo>^</mo></mover><mo>&gt;</mo><mn>0.5</mn></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mn>0</mn><mspace width="1em"/><mtext>otherwise</mtext></mrow></mstyle></mtd></mtr></mtable></mrow></mrow><annotation encoding="application/x-tex">\text{Decision Boundary}= \begin{cases} 1\quad \text{if }\ \hat{y}&gt;0.5\\ 0\quad \text{otherwise} \end{cases}
</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord text"><span class="mord">Decision Boundary</span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:3em;vertical-align:-1.25em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;"><span class="delimsizing size4">{</span></span><span class="mord"><span class="mtable"><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.69em;"><span style="top:-3.69em;"><span class="pstrut" style="height:3.008em;"></span><span class="mord"><span class="mord">1</span><span class="mspace" style="margin-right:1em;"></span><span class="mord text"><span class="mord">if </span></span><span class="mspace"> </span><span class="mord accent"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.6944em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.1944em;"><span class="mord">^</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.1944em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">0.5</span></span></span><span style="top:-2.25em;"><span class="pstrut" style="height:3.008em;"></span><span class="mord"><span class="mord">0</span><span class="mspace" style="margin-right:1em;"></span><span class="mord text"><span class="mord">otherwise</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.19em;"><span></span></span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></p>
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